University of Nigeria Research Publications
NWAORGU, George Iheoma
Aut
hor
PG/M.Sc/96/22687
Title
Interpretation of 2-D Seismic Reflection Data from Meren Field, Niger Delta
Facu
lty
Physical Sciences
Dep
artm
ent
Physics and Astronomy
Dat
e
December,1998
Sign
atur
e
INTERPRETATION OF 2 - D SEISI REFLECTION DATA FROMMEN FIELD, NIGER DELTA
NVYAORGU GEORGE IHEOMA R E G NO: ~ G / ~ k ? C / 9 6 / Z 2 6 8 7)
DEPARTMENT OF PHYSICS & ASTRONOMY UNIVERSITY OF NIGERIA NSUKKA
INTERPRETATION OF 2 - D SEISMIC REFLECTION DATA FROM MEREN FIELD,
NIGER DELTA
NVA ORGU GEORGE IHEOMA (REG NO: ~ G / ~ S C / 9 6 / 2 2 6 8 7)
I - . '. yL,
ARESEARCHPROJECTPRESENTED TO THE DEPARTMENT OF
PHYSICS AND ASTRONOMY UNIVERSITY OF NIGERIA NSUKKA
IN PARTIAL FULFILMENT FOR THE AWARD OF THE DEGREE OF
MASTER OF SCIENCE IN GEOPHYSICS.
CERTI FlCATlON
MR. NWAORGU GEORGE IHEOMA, a postgraduate student of
the department of physics and Astronomy with registration number
I'G/MSC1/96/22687 has satisfactorily fulfilled the requirement for course and
rese;uxh work for the award of the degree of master of science in
Geophysics.
'I'l~e work embodied in this project is original and has not been
submitted in past or ti111 for any other diploma or degree of this or any other
Ilniversity.
sufiervisor ' Prof. P.N. Okeke
DEDICATION
This research project is dedicated to
LORD MY REDEEMER
And
NWAORGU FAMILY.
ACKNOWLEDGEMENT
The contributions of several people made the completion of this
research project possible. The resource persons consulted have contributed a
lot and others have helped financially and morally.
I wish to express my sincere gratitude to these people especially my
supervisor Dr. J.U. Chukwudebelu. His efficient supervision, advice and
corrections added a great value to this research work. The 2 - D Meren Field
Data Interpreted was supplied by Chevron Nigeria Limited. In the course of
carrying out the research Mr. .N.A. Dada provided guidance and materials.
He is a retired Petroleum Explorationist of Nigeria Agip Oil Company
Limited. May God reward him. The special aid rendered by Dr. P.I.
Obiakor and Calister Odoemena was of immense value. Mr. Felix
Adindu rendered help in well log interpretation while Mr. Toyin Akinosho
made corrections on the interpretation of seismic sections. These are
Petroleum Expplorationists in Chevron Nigeria Limited. I wish to thank
Mr. Taiwo Rasaki of DPR, Lagos, Mr. & Mrs. R.M. Ogbeta for their
moral and financial support. I grateful to Cecilia Anih for the efficient work
done in typing this project. The contributions from the entire members of
Nwaorgu family especially my younger brother Sylvester Nwaorgu and
my mother Mrs. Emilia Nwaorgu are enonnous.
I am indebted to various authors and publishers whose materials have
been consulted in carrying out this work.
I thank all these people and mostly my GOD for giving me the
inspiration to pursue this course.
Nsukka December,l998
NWAORCU GEORGE.
ABSTRACT
The objective of this study is to carryout structural interpretation of 2 - D seismic reflection data. The interpretation is to locate possible structural
traps of hydrocarbon.
The data interpreted is a subset of 2 - D seismic reflection data obtained
fiom Meren field. The field is located in the offshore area of the western
edge of Niger delta basin. The seismic sections were examined and faults
were interpreted. The horizons mapped were selected by well log-to-seismic
correlation. The well log used was derived fiom well M - 73 located in the
survey area. Two horizons were interpreted and timed to produce time
contour maps.
The time contour maps were used to obtain a three dimensional view
of the subsurface layers mapped. It was assumed that, in a layered earth
where velocity is constant or velocity variation is small, the time for seismic
wave to travel to a layer is directly proportional to the depth of the layer.
Time contour maps were therefore used in studying the structures of the
formations mapped.
On horizon 1, six faults and seven closures were identified. The faults
are normal growth faults. The closures include simple rollover anticlines,
faulted anticlines, faulted closures and closures against faults. The faults are
growth faults and concave to the downthrown side. Reflection on seismic
sections and well log data showthat the closures are good hydrocarbon
traps. The locations of these closures were recommended for possible
drilling. Use of 3 -D seismic reflection data and cross sections to further
study the area were also recommended.
TABLE OF CONTENTS
CHAPTER ONE: INTRODUCTION
1.3.3 Structural style of Niger delta ................................
1.3.4 Hydrocarbon trapping mechanism ...........................
1.4 Geology of Meren field ........................................
i . .
"11
. . . 111
iv
v-vi
vii-x
CHAPTER TWO: BASIC THEORY OF SEISMIC WAVE
CHAPTER FOUR: PROCESSING AND INTERPRETATION OF
SEISMIC REFLECTION DATA
Introduction ---------------- ---- ------------------- - ----- ----- ---- -- Data Processing ------------ ---- ...................... - ------------- Fourier transforln ...................................................
Collvolution ............................................. ------------ Correlation ...........................................................
Processing sequence ................................................
Filtering ...............................................................
Delnultiplexing ------ ................................................. Field static comectjon ................................................
Common midpoint sorting ....................................... Velocity malysis/NMO correction ............................... Stacking ------------- ----- ------- --------------- ..................... Residual static correction ....................... ------ ------------- Migration ----------- --------- - .................... ------ -------------- Interpretation of seismic reflection data ........................... Introduction ------ -------------- -- --------------- ----- ------- - --------- Characteristics of seismic events ................................... Hydrocarbon habitats and trapping ................................. Evidence of faulting on seismic section ............................ Seismic stratigraphy ----------- - ---------------- --- ---- ----------- ---- Data used in seismic interpretation ................................. Seismic sections ....................................................... Vertical seismic profile --------- ------------ .......................... Synthetic seismogram ......................... --- ------- -- ----- ------ Base map ......................... ----------- ........................... Well log data -- ................................... - ..................... Seismic data interpretation sequence ............................... Selection of mapping horizons ----------- ........................... Interpretation of seismic sections ................................... Fault mapping and contowing --------------- -- -------- ---- ----------
CHAPTER FIVE: INTERPRETATION OF 2 -D SEISMIC
REFLECTION DATA FROM MEREN FIELD.
CHAPTER ONE
INTRODUCTION
1.1 Introduction
The interpretation of seismic reflection data which is consistent with
the geology of an area using available data is important in Petroleum
exploration. In oil and gas prospecting, the seismic method is more
suitable than other methods because of it's high ability to give details
of structure. Some of the other geophysical methods of exploration
include electrical method, gravity, magnetic and radioactivity
methods. Each method has it's advantages and disadvantages.
In general, seismology has to do with waves resulting from the
vibrations of the earth. Thus seismology involves artificially
generated and natural earthquake waves that penetrate well into the
earth.
In seismic reflection prospecting, sound is artificially produced
at or near the surface of the earth. The sound is produced using
chemical explosives or mechanical vibrators. The echo returned ti-om
the subsurface is recorded by detectors (geophones). The use of
computers makes it easy to record data in either digital or analogue
form.
The data is processed to obtain greater vertical and horizontal
resolution. The repositioning of the data done during processing gives
a better picture of the subsurface. During acquisition and processing,
the unwanted seismic energy reflected (noise) is attenuated by
filtering. The primary reflections (signals) from bedding planes are
enhanced. Seismic data acquisition and processing is done with the
aim of maximizing signal to noise ratio. The seismic reflection data
acquisition technique is an application of the principle of "echo
acoustics" therefore processing and interpretation are based on wave
equation and wave characteristics of seismic events. Reflection
occurs where there is change in acoustic impedance/velocity across
the interface.
The interpreter uses the regional geology, seismic data, well log
data, gravity anomaly and other relevant data to locate hydrocarbon
traps. The alignment of reflections and splitting of wavelets on a
particular horizon is used in delineating anticlines, synclines, faults
and other structures in the survey area. The use of amplitude
preservation processing has given birth to direct detection of
hydrocarbons on seismic section using "bright spots" and "dim spots".
In this regard facie analysis using 3 -D seismic data is very important
in interpretation of seismic data. Interpretation gives information on
the hydrocarbon bearing sand, the structural traps and positions of
faults. This becomes a guide in positioning and drilling of wells.
In this project, based on the available data, "Time contour
maps" are produced for the horizons interpreted from the seismic data.
This was used, to obtain areas of possible hydrocarbon accumulation,
the fault positions and trapping mechanism of the subsurface mapped.
The subsurface geological map is an important instrument for
discovery of hydrocarbons during exploration.
1.2 Obiective and scope of study.
The objective of this study is to carryout the structural
interpretation of an already acquired 2 -D seismic reflection data fiom
Meren field in the offshore Niger Delta basin of Nigeria. The
structural interpretation will give possible location of hydrocarbon
accumulation and leads to recommendation of optimal drilling sites.
The scope of this project is within the area covered by the
seismic sections available. This consists of nine dip lines and four
strike lines which were used for the study. The regional geology of
Niger delta will be combined with the deductions from the interpreted
data to make recommendations and draw conclusion.
1.3 Geolow of N i ~ e r delta
1.3.1 Regional setting and basin formation.
The Niger delta is one of the ten major sedimentary basins of
Nigeria. The others are Abakaliki basin, Anambra Basin, Benue
trough, Bida basin, Bornu-Chad basin, Dahomey basin, Gongola
basin, Sokoto basin and Yola trough. These onshhore basins occupy
about half the total area of Nigeria (Whiteman 1982). The basins are
delineated by three main areas of basement complex. These are
Western end of the Cameroun volcanic zone, Northern Nigeria massif
and the eastern end of West African massif. The basins and basement
complex are shown in figure 1.1 .
The -Niger Delta complex basin is situated on the Gulf of
Guinea on the west coast of Central Africa. It built out into the
Atlantic ocean at the mouth of the Niger-Benue river system during
the tertiary @oust and Omatsola 1990). The maximum sediment
thickness is at the central part of the delta within the greater Ughelli
megastructure. The thickness is about 12 kilometers.
The formation of Niger delta basin and others started with the
break of the central African-south American part of the Gondwana
super continent. This took place in the Mesozoic. It is along a series
of rift zones of different orientations that met in a triple junction on
the present gulf of Guinea. Two of the anns, which followed the
southeastern and southwestern coasts of Nigeria developed into
collapsed continental margins of south Atlantic. The first sediments
of the cretaceous to tertiary cycle accumulated during the rift-fill
phase. Thick successions of marine and marginal marine clastics and
carbonates were deposited in a series of transgressive and regressive
phases. On complete separation of the continent, the sea transgressed
inland to Benue trough which is the third arm due to subsidence of the
continental basement.
The present Niger delta basin is built on the collapsed
continental margins of the south Atlantic. The core of the delta is
located over the site of the triple junction. The bulk of sediment
supply fiom the north and east is through the Niger-Benue river in the
tertiary. The Benue and Cross rivers supplied substantial amount of
volcanic detritus fiom Cameroun volcanic zone since the Miocene . The Niger delta has prograded into gulf of Guinea at a steady rate.
This is due to drainage area, basement subsidence, and eustatic sea
level changes.
Presently the Niger delta is typically wave and tidal dominated.
It appears to be constructive at the centre and destructive at the flanks
(Nedeco 1959)where it is sandy. The lower plain consists mainly of
distributary channels of rivers surrounded by fiesh water swamps.
The destructive part of the delta are salt water mangrove swamps with
greater tidal influence. Long shore currents carry sediments off the
area form sandy beaches, beach bridges and offshore bars along coast
flanks (Burke 1972). The marginal areas of the delta suffer
encroachment due to lack of sediment supply.
The submarine portion of the delta consists of shallow shelf
which gradually merges into a long continental slope. The upper part
of the slope is marked by a zone of faulted sediments, clay walls and
diapirs known as distal belt. This is the outermost portion of the
developed part of the delta.
The trend of development of the Niger delta is a major factor in
the stratigraphy and structure of the region.
1.3.2 Stratigraphy of Niger delta.
The Niger delta is composed of regressive sequence of clastic
sediments developed in a series of offlap cycles. The delta shows a
tripartite lithostratigraphic successions in which regressive sequence
is demonstrated. The well sections in figure 1.2 shows the division of
the overall regressive scheme into gross lithofacies units. Formal
stratigraphic names are given to these unit; thus we have fkom the top,
continental alluvial sand (Benin formation), the paralic clastics
sequence (Agbada formation) and the marine shale (Akata formation).
The Akata formation extends to the basement rock. It is a massive
monotonous marine shale. The paralic facie on top of Akata
formation consists of shallow marine and fluvial sands, silts and clays
which are interbedded. The non marine continental sand on top of
these formations is massive. Pre-deltaic basement indications are seen
Fig 1.2 Well sections showing regressive scheme of the Niger delta @oust and Omat sola 1990).
on seismic data only along the northwestern and north-eastern basin
flanks. It is also seen below the continental rise offshore. The deltaic
facies range in age fiom Eocene in the North to miocene-pliocene in
the south.
The detailed stratigraphy of Niger delta is complex. The delta
is affected by synsedimentary faults, the rate of sediment supply and
subsidence, then tidal waves. These control the progradation of the
delta. The Niger delta is divided into major sedimentary units by the
synsedimentary faults giving rise to depobelts. These depobelts are
shown in figure 1.3 with the age of the deltaic sequence. These are
northern delta depobelt (P450-P560) or late Eocence to oligocene,
Greater ughelli depobelt (P650-P680) or early miocene to middle
miocene, central swamp 1 depobelt (P720-P740) or middle miocene,
central swamp I1 depobelt (P770) or middle miocene, coastal swamp I
depobelt (P 780-P820) or middle miocene to late miocene, coastal
swamp I1 depobelt (P830-P840) or late miocene, offshore depobelt
(P900) or quaternary and the delta edge @oust and omatsola 1990).
In each depobelt, the tripartite regressive sequence forms an integral
delta unit of distinct age. Each depobelt contains one or more
paleontogically distinct transgressive shale horizon. This represents
interruptions in the overall regressive sequence. These transgressive
shale horizons are probabaly related to sea level rises. The lithofacies
do not have distinct boundaries which makes it difficult to define
separate formations.
The major lithofacie units of the Niger delta are shown in
fig. 1.4. It illustrates the diachronous nature of these lithofacies .
LATE
QUATERNARY .-- PLIOCENE
- W Z W
-
-
- OLIGOCENE
LATE
EARLY
PALEOCENE ---
IF>L'J[-- - ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ---A FACES - - - - - - - - - . - - - - - - - - . - - - - - . . . . . . . . . . . . . . . . . . . . . .
1 I I I u E X T E M OF EROSIONAL TRUNCATDN
Eig 1.4 The tripartite sequence of major lithofacies units ofthe Niger delta @oust and Omat sola 1990).
The Akata formation which is composed of shales, silts and
clays is at the base of the delta sequence. It contains a few streaks of
sand. The sand is turbiditic in orgin and were deposited in the
holomarine environments. The shale ranges from paleocence to
Holocene in age. They crop out offshore in diapirs along continental
slope and onshore in the northeast of the delta (Imo shale). The top of
this formation is the economic Basement for oil. The deeper
formation contains gas dissolved in oil field waters under high
pressure. The onshore is rich in benthonic foraminefera. Sand and
silt beds break the uniform shale.
The Agbada formation is the hydrocarbon prospective sequence. It
consists of sand, silts and clays in various proportions representing
offlap units. They were deposited in delta fronts, delta topset and
fluvio-deltaic environments. The alternation of fine and coarse
clastics provide multiple reservoir seal couplets. This is present in all
the sedimentary units. The age ranges from Eocence to pleistocene.
The sand consists of lignite streaks and limonite. The thickness of
Agbada formation is about 3000m. In this formation pre-Miocene
reservoir rocks are deposited as con ti nu^ sand, point bars and
channel sand. Miocene and younger rocks were deposited as barrier
bars. The Agbada formation lies between Akata and Benin formation
(weber and Dakoru 1975).
The Benin formation is the uppermost unit. It is made up of
massive fresh water bearing sand and gravel. The sand was deposited
in alluvial environment. The Benin formation sand is thinner in the
coastal swamp and in the offshore depobelts. It's maximum thickness
is about 2000m. Little oil is found in this formation (short and stauble
1967, Avbovbo 1978).
One characteristic which distinguishes these formations is the
sand to shale ratio. The top of Agbada formation is the base of fi-esh
water inversion while the base of Agbada formation is the on set of
hard over pressured zone. This marks the top of Akata formation
which continues to the basement rock. A shematic structural section
showing relationships of the tripatite division of the tertiary sequence
is shown in figure 1.5 @oust and omatsola 1990).
1.3.3 Structural style of the N i ~ e r delta.
The dominant direction of movement and involvement of
basement rocks are important in a sedimentary basin. In petroleum
exploration, it dictates the extent sediment is structured into potential
traps and amount of closures at a level. The basement rock influences
the regional and local structural pattern.
The tectonics of Niger delta are limited to extensional
deformation and minor basement involvement. - The most visible
extensional faulting occurs in the paralic clastics (Agbada formation).
The marine shale (Akata formation) has obscure structure while the
continental sand accumulated over each growth fault trend. Growth
faults dominate the structural style. This is attributed to the
movement of over pressured, ductile marine shale combined with
slope instability. The deformation that creates structures capable of
trapping petroleum is cold deformation in which temperature and
pressure are not extreme. Shear failure follows fracture propagation
in an elastically deforming medium. The faults found in the Niger
delta are mainly listric and normal faults.
The growth faults initiate when sand prograde over
uncompacted shale. The local overburden due to density contrast
between shale and their overlying sands creates gravity instability:
causing growth faults. The shales are laterally displaced under
increasing sand weight. Faulting starts as a steep shear plane at the I
upthrown side of the depocentre. The shear plane then separates as
growth faults due to higher sediment infill in the down block of the
structure close to the fault. The dip magnitude increases downward in
a counter fault direction.
Growth fault index = unit thickness of down block
Unit thickness of upblock.
The vertical component of the faulting process is generally
combined with a horizontal displacement of the down block due to
regional delta slope. This gives rise to formation of rollover
anticlines. The Niger delta rollover anticlines shows that the crest
shifts with depth (Evamy et al, 1978). The rollover anticlines shows
as gentle undulations due to differential compaction.
Mud diapirs occur on the landward side of growth faults in each
depobelt. This restricts' sedimentation on the upthrown side of the
fault but enhances sedimentation on the downthrown side. The mud
diapirs located on the ,seaward side of the growth fault produce
collapsed crest structures. This causes variation of sand deposit
thickness in the downthrow. The principal types of structures found
in the various depobelts of the Niger delta are shown in figure 1.6.
The structural style in the depobelts differ a little from each other.
The preponderance of anticlines and faulted anticlines in the older
depobelts gives way to more complex structures like collapsed crests
in the coastal swamp and offshore depobelts. The structural style as
: :! U t-
w 8.9 D
-! Z m m s ;r v :: '3- m 0 c 0 P
U D Z D w
D 1 rn U
6 2 - z 4 x m
U n
I I?
I P 1 0 b r U m 0 2 0 z (I)
D
0
I m
F t 0 4 I n X 2 m U U)
w
(I)
I 4
a n 3 . II (I) 4
P r P M - U
z
observed in various depobelts is shown in figure 1.7. The Northern
delta depobelt and the delta edge westward is dominated by anticlines
and faulted anticlines. In the central delta depobelt, faulted anticlines
dominate with few collapsed crest structures, while in the coastal
swamp and offshore depobelts there are more complex structures of k-
type footwall closures and collapsed crest anticlines.
1.3.4 Hvdrocarbon trapping mechanism.
The sealing capacity of faults in the Niger delta appears to
depend on the amount of the shale smeared into the narrow fault zone.
This depends on the amount of clay layers over the throw of the fault.
A fault is sealing if it has been passed on the down thrown side by an
interval of more than 25% shale @oust and omatsola 1990). Sealing
capacity increases with increase in percentage of shale. In some oil
reservoirs, overpressure makes some rollover anticlines to be full of
oil between demarcating faults. Migration of oil in the Niger delta is
by spilling up through the narrow conductive fault zones. The
blocking off of delta sequence into cells by growth faults cause lateral
and vertical variation of hydrocarbon properties suggesting little
megration.
According to Doust and omatsola (1990), the trapping
structures may be classified into complex structures, anticlinal dip
closures, up thrown fault closures (foot wall) and down thrown fault
closures (Hanging wall). This is shown in fig 1.8.
In anticlinal dip closures, trapping is by means of simple
closure independent of faults. This is of three types, unfaulted simple
dip rollovers, dip closures where fault though present contributes less
than 15metres to the closure and faulted anticlinal closures where dip
closure is these dissected by synthetic and antithetic non sealing
faults. Closure here is limited to dip element.
In down thrown fault closures, trapping- relies on combined
dip/fault closure on the down thrown side of a sealing fault. In this
case the fault plane and sediments dip are in the same direction. This
may be where the fault dependent element exceeds 15m of vertical
column or where the bed is juxtaposed against over pressed shales in
the up thrown block.
Trapping in the up thrown fault closures is by combined
dip/fault closure on the up thrown side of the sealing fault. In this
situation the sediment dip and the fault plane are in opposite
directions. The situation may be where the upthrown side of a north-
dipping antithetic fault lies on the south flank of a rollover structure.
It may also be where the upthrown side of a south -dipping synthetic
fault lies on the northern flank of a rollover structure. Also the
upthrown side of a structure building fault if deep may he below the
structure in the overlying downthrown block.
1.4 Geology of Meren field
The g e o h of Meren field is derived fiom the regional geology
of Niger delta west.
The field is shown on the fault map of Niger delta in figure 1.9.
The field lies in the delta edge at the northwestern flank of the Niger
delta basin. It is an offshore field at the mouth of Benin river. The
field lies outside the two lobes of the southern offshore depobelt of the
Niger delta since it is located at delta edge. The structures in the delta
edge differs fiom the structures within the main offshore depobelt of
the Niger delta at the southern part.
The structural style of the field is dominated by antidinal dip
closures and closures against the downthrow of growth fault found in
the region. This is illustrated in figure 1.7. The structure 'at the delta
edge differs from the complex structural style of the coastal swamp
and southern offshore depobelts. In the coastal swamp, collapsed
crest closure and k-type footwall closures dominate. The trapping
morphology of the field is that of simple unfaulted rollover anticlines
and faulted anticlinal closures. However, the presence of complex
structures within the field cannot be ruled out since it lies offshore.
The stratigraphy follows the tripartite sequence of marine shale
(Akata formation), paralic clastics (Agbada formation) and continental
alluvial sand (Benin formation). In the field, the continental alluvial
sand is thick as in the delta edge. Diapirism is not well pronounced as
in the southern offshore deposbelt hence the absence of complex
structures. There are growth faults which are similar to the faults in
the northern depobelt.
The geology of a given area determines the reflections on the
seismic section. The propagated acoustic wave is reflected at
stratigraphic boundaries. Faults cause diffractions and change
alignment of primary reflections. . Data acquired by transmitting
seismic wave through the earth depends on the nature of the
subsurface. It is therefore imperative to understand the theory of
seismic wave propagation through the earth. This will make data
acquisition and interpretation to be consistent with the geology of the
survey area.
CHAPTER TWO
BASIC THEORY OF SEISMIC WAVE PROPAGATION
Introduction
The elastic theory of waves plays an important role in data
acquisition and processing.
The formulation of wave theory combined with spatial
convolution (signal theory) is significant in processing of seismic
data. Complex seismic response is understood using elastic modeling
schemes. One way elastic wave equation is used, is in wave equation
migration scheme. The acoustic parameters of compressibility and
density which determine propagation velocity are obtained using wave
equation. During acquisition, seismic source and detector positioning
are based on the wave theory of propagation, transmission and
reflection of seismic waves. We now present the general theory of
seismic wave propagation. The treatment given below follows that of
sheriff and Geldart (1982).
2.2 Fundamentals of elastic wave propagation
2.2.1 Theory of elasticity
The elastic behaviour of rocks is described here in terms of
stress and strain. Stress is defrned as force per unit area while linear
strain is defined as extension per unit length.
b Fig 2.1 Components of stress for faces pemendicular to x - axis.
Fig 2.1 shows a small element of a rock under stress. The forces
acting perpendicular to each face of the cuboid respectively give rise
to normal stresses designated as p, p, and p,. P, is the x
component of the stress acting on the face perpendicular to x
direction. P, is the y component of the stress acting on the face
perpendicular to the y direction. P, is the z component of the stress
acting on the face lying in a plane perpendicular to z axis.
Similarly tangential forces acting on the body give rise to
shearing stresses pm, p , p,. P, is the y component of the stress
acting on the side lying in a plane perpendicular to x axis. P, is x
component of stress acting on a side lying on a plane perpendicular to
%axis. P, is x component of stress acting on a side lying on a plane
perpendicular to z axis and P, is the z component of the stress acting
a side lying on the plane perpendicular to y axis.
Under equilibrium condition the stresses are balanced and the I
body is stable. When an external force is applied, the stresses become
unbalanced. They oppose each other causing changes in shape and
size. Opposing shearing stresses give rise to a couple.
For example rotational equilibrium about the z-axis is
I& dydzdx = P,dxdzdy, where dxdydz is an element of volume. It
follows in this case that p, = pm. It can be shown in general that
under equilibrium condition
Pij = i # j
Fig:2.2 .\nnlvsis of 2-D strain. k In fig: 2.2, the rectangle PQRS lies in the x-y plane. When
stresses are applied, the displacement components of PP' are u and v
respectively. In a situation where u and v have different values,
changes in size and shape occur (strain).
Let u=f (x,y) and v = f (x,y); then the cordinates of PQRS and
P'Q'R'S' are as follows:
Q (x+dx,y): Q' (x+dx+u+&dX y+v+& dx) 6x 6x
S (x, y+dy): S' (x+u+&dy, y+dy+v+&dy) 6~ 6~
R (x+dx, y+dy): R' (x+dx+u+&dx+bdy, y+dy+v+6xdx) 6x 6y 6x
In the present discussion we assume that the terms
6m-6~ and 6~ and 642_ are small enough for their powers and 6x 6y 6x 6y products
to be neglected. Hence we make the following deductions.
6d6x and 6v16y are fractional increases in length in the x and y
directions respectively. 61 and 62 are infinitesimal angles equal to
6d6x and 6v16y respectively. The right angle at P decreases by
61 +A and is rotated counter clockwise through 61 -& . The quantities 6dSx = e, and 6vI 6y = e, are normal strains. The s h e e n g strain e, = (6vI6x +6d6y. The rotation of the body about z axis is given by 4 = (GvlSx - 6u by). In 3-D using displacements u,v, and (3, we have e, = 6u/6x, eyy = 6v/6y, ezz = 6W6z ... ...... ... (2- 1
The components of rotation of the body about z axis are
Q = y x S where S= iu +jv + ok.
Dilatation 8, is defined as the change in volume per unit volume. Thus,
Hooke's Law
It states that for small strain, the given strain is proportional to the
stress producing it. When several stresses act, each strain is a linear
function of all the stresses and vice versa.
For elastic energy to be a function of strain, we must have C, = C,
In isotropic solid, only two elastic constants remain since the
coefficients are independent of set of axes chosen. These constants
are denoted by h and p. Where
C12= C13=C21=C23=C2S =C32=C31 = h
= cSS =C(j6 = p
Cll =Cu=C33 = h + 2 p
we can then state Hooke's law as
Pii = he +2&i ................. (2.5)
Pij = p eij ......................... W )
h and p are lame constants. The other elastic constants are youngs
modulus, E, poisson's ratio, a and bulk modulus, k. The relationship
between these elastic constants are given as follows (sheriff and
Geldart 1983).
E = P, /em = p (2p=3h) '/h+p ................ (2.7)
CJ = - e,le, = -e,/ e, =A A jp ............... 0 2 (2.8)
When a solid is subjected to uniform hydrostatic compression, P, = P, = P, = -P and fractional change in volume equals - (e,+e,+e,)or -8.
This shows the changes that occur on the solid when force acts on
it. Forces acting on the layers of the earth causes a change in the
elastic properties. This makes it possible for seismic wave
propagate through the medium. . . -
?* . . - - - - . .
. . . I
The wave equdon. mi-
Fig. 2.3 Stresses on faces perpendicular to X- axis.
Using fig.2.3 we obtain equations of motion in an elastic homogenous
isotropic medium. The stresses on the fiont face are
Pxx + P n +&zx+jXand Pyx + &yx&
6, - 6, 6, The stresses on the rear face are P, , P, and P,. The net unbalanced stresses are therefore P, + 6 b - d)( Pn + Gp,h(and P, + 6padX -
6x 6 x 6 x respectively.
These stresses on the area dy dz and affect the volume dxdydz. The
net force per unit volume in X direction is given by 6pd6x (dxdydz)/ dxdydz
The net force per unit volume along x direction is 6pd6x. Similarly we obtain for y and z directions 6g,&x and 6b&x - respectively. The total force per unit volume in x direction is (6g,+ - 6gz+ 6ga - )
6, 6, 6, For motion along x axis Newton's second law of motion is
e 6 2 ~ - = 60 , + 6g!, + 6gE st2 6x 6y 6z
whereg = density 6g=+ d& + 6p&
st2 6x 6y 6z
es&= 6 h + 6&. + - .............. (2.12) st2 6x 6y 6z Expressing the above equations in terms of strains we obtain
In terms of displacement the force is
In a homogenous isotropic elastic substance we obtain the wave
equation by differentiating equations 2.14, 2.15 and 2.16 with respect to
x,y,z respectively. Summing up we obtain
where a is propagation velocity and z2 916t2 is being propagated. The
wave is dilatational (P) wave. To obtain the shear wave equation we differentiate equations 2.15 and 2.16 w.r.t z and y respectively to obtain.
Subtracting equation 2.18 from 2.19 we obtain
Similarly we obtain R, and R ,. Where P is the propagation velocity of the rotation d RJ6 t? being propagated through the medium. To obtain the solution of the wave equation, we state the standard wave
equation as ti2 Y / v2 6 t? = V ~ Y ........... (2.22).
where Y is the wave function and V is the velocity of the wave. The general
solution for a plane wave travelling along x axis is given by
Y = f (x-vt) + g(x+vt) ................ (2.23).
In spherical co-ordinates the solution is given by
1 62 Y = 1_ ~ ( 2 6 ~ ) + 1 6 ( s i n e w + &Y --
v2 6 t? [6r 6 r sine 6 8 6 8 ~ i n ~ 8 6 4 ~ ... (2 .24)
When the wave motion is independent of 8 and 4, Y becomes a function of r and t, equation 2.24 simplifies to
The general solution of equation 2.25 is
rY = f (r-vt) + g (r+vt) ............ (2.26)
The wave equation can be written in terms of scalar potential of
displacement 4 and vector potential of displacement Y. The use of vector
and scalar potentials enables the wave equation to express displacements u,
v, W and the velocities u', v', and W' in terms of potentials. We have
4 (x,y,z,t) and Y ((x,y,z,t). We express
Using these relations we obtain in the wave equations 2.17 and 2.21 respectively as
The wave equation is easier to analyse for the propagation and
reflection of waves when stated in terms of potential function.
The dilatational wave and shear wave are bodily elastic waves ; they
propagate through the body of the earth. However rotational waves
are not transmitted through a body of zero rigidity such as fluids.
Also P-wave velocity (a) is greater than the shear wave velocity p since a = 843 for materials whose Poisson ratio is above 0.25.
Transmission and reflection of bodily elastic waves.
Fig 2.4 Two laver medium in welded contact.
In fig 2.4, M, and MI represent two layers in welded contact
along a horizontal boundary surface. Consider a plane wave incident
in M and reflected at the boundary. x, y and z are perpendicular to
eachother. The wave is incident in the direction oy and
perpendicular to the direction ox. For a simple harmonic wave, the
solution which corresponds to the waveform is
h l ( z ) = CIexp( -~kS~z )+F~exp( iks~z )
Due to reflection back into the medium and transmission across the boundary, the displacement can be expressed as
Where 4 is the scalar potential and ty is the vector potential. For a
3- D displacement of plane wave, we have
u, v and W satis@ the equations of simple harmonic wave if
ti2 = p 2 v 2 ~ - st2
and
in both media M and MI. The relevant solutions of equation will
contain no term in y. x will enter as a factor of the term e - ' ('*') I
\
Fig 2.5 Reflection of body waves. L . P U N S OF WAVE FRONT
, -.
In fig 2%
= (c2-9) ((At )2
2 tan e = - a2 = c2 - g S ( A ~ ) 2
cose = VAtlc At = v/c
v - - Ccose = Csini ............ (2.34)
1/C is a constant for all waves involved.
cose ==f = c m = cosf, = 1 '. - a P a I P 1 c
The general solution for p waves in medium M is
4 = Ao exp {ik (ztane + x-ct) ............ (2.35)
where k has been used for K, and is given
Ka2xcoselh = K cose ............... (2.36)
Kz = 2nsine/h = ktane ............... (2.37)
For reflected P waves in medium MI the solution is
4 = A exp {ik (-ztane +x -ct)) ............... (2.38)
and
t+ = ~oex&ztane + x-ct)) + Aexp (k(-ztane +x-ct)
for incident P wave.
For incident SV wave we have
y= Bo exp (ik(ztane+x-c-ct) {+ Bexp {ik(-ztane +x-ct}
when SH wave is incident we .............. (2.39)
V = Co exp {ik(ztanf +x-ct))+Cexp{ik(ztane +x-ct)}
When P is incident Bo = Co = 0
When SV is incident Co = Ao = 0
When SH is incident Ao = Bo = 0
To determine the coefficients A,B,C,Ao) Bo and Co
respectively we apply boundary conditions. The conditions apply to
continuity of displacement and stress across boundary at all places and
times.
For incident SH waves Ao = Bo = o and pfo. The boundary
conditions which involve 4 and y then show that A, B, Al and B1
have no dependence an Co and the relevant solution is accordingly of
the form.
In medium M V= Co exp(ik(ztanf +x-ct)) + Cexp (ik(-zatnf +x-ct)
........... (2.41)
and in medium M1
If C L ~ O for continuity of displacement at the boundary
for continuity of stress, we differentiate equations 2.41 and 2.42 wrt z
and put z=o to obtain
from Equations 2.4 1 and 2.42
C - - - -1- C -- co ptanf - pltanfl 2ptanf = ptanf + pltanfl ............... (2.45) using sini = cose = constant. We have v v sini = cose - (2.46) - ............... v P 1
In the case of normal incidence we have
C = -1- C = C', --
............. PP1 -PIP 2PP 1 PPl+ PIP (2.47)
The above solution shows that when incident wave is of SH type, the
reflected and refracted wave can only be of SV and SH type.
We now consider a situation in which P- wave is incident on a free
surface. The reflected waves obtained are P and SV waves.
Fig. 2.6 Incident P - waves on a free surface.
In fig. 2.5 the interface is horizontal and coincides with the x-y plane.
The z axis points in the upward positive direction. We use the elastic
wave equations
The solutions to these equations in medium M are
4 = Ao exp { k (ztan+x-ct)) +Aexp {ik(-ztane +x-ct)) ......... .(2.49)
Y = Bexp {ik(- ztanf + x-ct)) .......... (2.50)
V = Cexp {ik(- ztanf + x-ct)) ........... (2.51)
The boundary conditions are
(1) The stress components PZy , P, and P, must vanish at the boundary.
.... P, = p6v 1 6z = PC(-iktanf) exp {ik(-ztanf +x-ct)) = 0 (2 .52)
By differentiating and equating to zero we obtain
& = A (-iktanep exp (-ik ztane) exp:d(x-ct)) + 6z2 Ao ( ~ k t a n e ) ~ exp (-ik ztane) expid(x-ct)) ....... (2.54)
& = A (ik)2 exp (ik ztane) exp {k (x-ct)) + 6x2 Ao ( ikp exp ( ik ztanf) exp {ik (x-ct)) ....... (2.55)
......... & = B (iktanf)(ik) exp (-ik ztanf) exp {ik (x-ct)) (2.56) 6z6x P, at z=o gives assuming h=p
P, = h { ~ ( i k ) ~ + ~ o ( i k ) ~ +(-iktane)2 A+(ilctane) Ao ) + 2p {A-(iktane)2 + Ao(ktane)' -B(-iktanf)(ik)) = o ... (2.57)
= (Ao+A)+(A+Ao)tan2 e+2(A+Ao) tan2 e + 2B tanf = o
hence
(A+Ao) (l+3 tan2 e)+2Btanf = o
62b = A (-iktane) (ik)exp (-ik tane) exp {ik(x-ct)) + 6z6x
.... +Ao (iktane) (ik) exp (-ik ztane) exp {ik (x-ct)) (2.58)
i& = B (ik) exp (-ik ztanf) exp {ik (x-ct)} ......... (2.59) sx2
a t z = o
p = )J{2(-ik)tane ) (ik)A+2Ao (iktane)(ik)- B(ik)' + B (iktanf) ) = o ...( 2.60)
from Equation 2.57
........ from Eqn 2.60 Ao-A = - ~ ( t a n ~ f - 1) (2.62) 2tane
Adding Equations 2.61 and 2.62 we obtain
Ao = - Btanf - ~ ( t a n ~ f -1) ......... (2.63) 1 +3 tan2e 4 tane
hence
B = - - (4 tane) (1 +3 tan el Ao 4tane tanf + (1+3tan 'e) (tan2 f-1) ............ (2.64)
Using snells law and poission relation
Sini = cose and k =p , a 4 4 3 - v v
We obtain from equations 2.61 and 2.62.
B = Ao
- 4tane (1+3tan2e) 4tane tanf +(1+3tan2e $ . . . . . . . . (2.65)
A = B (ctan2 f-1) (1+3tan2 e) - (4tanf tane))
4 tane (l+3 tan2e)
substituting B in equation (5)
A - - Ao ... ... . (2.66)
2 2 4tane tanf - (1+3 tan e) 4tane tanf +(l+3tan2e )
we note from equations 2.61 and 2.62 that, at normal incidence of P
waves e = d 2 cos2 e = 3 cos2f = o and for grazing incidence e = o, B
= o, in both cases. These are the only conditions in which there is SV
reflected waves*fiom equation 2.66 A vanishes if
(1+3tan2e)l = 4tane tanf
using cos2 e = 3cos2f we see that this equation has two relevant roots
e= 12.8 O and 30 "- For these angles of emergence there are no
reflected p waves.
2.2.4 Surface waves.
In an infinite, homogenous, istropic medium only p and s waves
which are bodily elastic waves exist. When there is a surface
separating media of different densities or elastic properties, surface
waves exist.
Seismic surface waves are guided along the surface of the earth
and the layers near the surface. They do not penetrate into the earth.
Their amplitude decrease with increase in depth from the surface.
Two main types of surface waves are Rayleigh wave and love wave.
Love waves occur when there is general increase in s-wave
velocity with depth. This involves transverse motion (SH) which is
parallel to the surface of the earth. They can only be recorded by
horizontal geophones hence of much less importance in seismic
exploration.
Rayleigh waves propagate close to the surface of a semi-infinite
medium. The particle motion is confined to a vertical plane
containing direction of propagation. The particles describe a
retrograde near the surface of uniform half space. It can therefore be
recorded by both vertical and horizontal seismometers.
In this section, we derive expressions for the propagation of
surface waves along a plane horizontal boundary separating two
homogenous perfectly elastic media in welded contact and apply it to
a situation where Rayleigh waves exist.
Fig 2.7 Two media separated bv a horizontal boundaw in welded
contact.
In fig 27, MI extends upwards infinitely while M extends downwards
infinitely.
Consider a wave travelling in the direction ox in such a condition that
(1) The disturbance is largely confined to the vicinity of the boundary.
(2) At any instant all particles in any line parallel to oy have equal
displacement.
The first condition shows that it is a surface wave while the second
condition shows that it is a plane wave. Therefore all partial derivatives
w.r.t.y are zero.
The assumptions shows that the components of displacement u, v and
W satism Newtons law of motion given in terns of displacement in 2.14,
2.15 and 2.16 hence from 2.26a we see that, u, v and cl> in medium M
hence
we then have
substituting for u and o in terns of potentials (equation 2.26a) we
have
From equation 2.67 we have
From 2.68 and 2.69, equation 2.14 becomes
The above equation is satisfied if the following relations hold in medium M.
similar relations hold for M1 with al, Pl and pl
To solve the above equations we put
+ = f (z) exp {ik ( x-ct)} ............... (2.74)
v = g (z) exp {ik (x-ct)} ............... (2.75)
v = h (z) exp {ik (x-ct)} ........... (2.76)
for medium M. similar relations hold for medium M1 with f, g, and h
replaced with fl, gl and hl. This will lead to a particular solution
corresponding to a group of SH waves of wave length 2 d k travelling
with speed C.
introducing r, s, rl and sl where
substituting 2.74, 2.76 into 2.71 and 2.73 in a typical case for the medium'
M1, we obtain
but v = hl (z) exp {ik (x-ct)}
differentiating v w r t to t we obtain
6v = (-kc) hl (z) exp {ik (x-ct)} - 6t
s2v = (ik)2 h (z) exp {ik (x-ct)} .............. - (2.79) sx2 s2v = k2 c2 hl (z) exp {ik (x-ct)} ........ - (2.80) st2
s2v = - . hl (z) exp {ik (x-ct)} 6z2 8 2
comparing 2.78 and 2.80 we have
k2 c2 hl (z) exp {ik (x-ct)}= p2 {- k2 hl (z) + d2 hl (z) }exp ik (x-ct} &-
............ d A l + (z) hl k2(& 1 ) = o (2.81) d 2 p2
+hl P Sl2 = 0
cb2 solving we obtain
@+ hl Ps12) h1=0
The general solution is
hl p) = Cl exp ( -ik sl z) +Fl exp (ik slz) ......... (2.82)
for the effect to be essentially a surface one hl (z) must diminish
indefinitely with increasing distance from the boundary. This will be
the case if hl (z) contains an exponential factor in which the exponent
is real and negative hence s, r and z are inaginary. Also constants
corresponding to C1 must vanish in medium M1 as those
corresponding to F1 vanish in medium M.
The form of solution in M is therefore
4 = A exp {ik(-rz + x - ct)}
w = B exp {ik(-sz + x -ct)}
V = (exp (ik (-sz + x -ct}
The solution in M1 is of the form
4 =Dl exp {ik (rl z + x -ct)
w = El exp {ik (rl z + x -ct} ........... (2.85)
v = F1 exp {ik (sl z + x -ct} ........... (2.86)
where A, B, C, D, E and F, are constants and r, s, rl and sl are all pure
imaginaries.
The boundary conditions are that displacement at boundary surface
are continuous at all times and places. The stress across boundary surface is
continuous at all times and places
In medium M we differentiate 4 wrt x and wrt z in equations 2.83
and 2.84, then add to obtain at t = o, z = o, x = o
U = Aik - Bisk ... ... ... ... .. (2.87)
In medium MI, similarly using 2.85 and 2.86 at t= o, z = o and x = o
we obtain u = Dl ik + El ik sl . ... ... ... ... ... (2.88)
Equating 2.87 and 2.88 for continuity of displacement
For continuity of o at boundary we have
-Aikr-Bik=D1ikrl-El ik
for continuity of v we have c = F1 ........ . . ........ (2.92)
considering continuity of stress, the stress components involved are P,, P,,
and P, using the stress - strain relation
Pij = + 2pe ij
we obtain in medium M
pzz. = p ( 2 a -& +&) . . . . . . . . . . . . . (2.94) 6z6x 6x2 62
- Pzz - P& ... ... ... .... (2.95) 6z
Substituting from 2.83 and 2.85 into 2.93,2.94 and 2.95 we obtain after
solving, at t = o, z = o x = o
pm = - I Z ~ { h ( 1 + ? ) + 2 ~ ? ) - 2 p ~ P s ... . .. . .. ... . (2.96)
similarly for medium M1 at t = o, z = 0, x = 0,
- PZ - - IZD~ (hl+hl? + 2p1 1: )+ 2p1 E]I? sl ... ... .. . ... (2.97)
using
a2 = h+2p and p2 = p/p P
equation 2.96 becomes
from equation 2.97, we have in medium M1
Equation 2.98 and 2.99 we have for continuity of stress
.......... (2.100)
Similarly,continuity of stress P, in M and MI we have
[ - 2 r ~ - ( l - S ~ ) ~ ] p2 p = [2rlD1- (I-S21)~l] p2 pl
for continuity of stress p,, we have
-pCikS = p1 F1 ikSl
or -SC p2 p = s1 F~ p12 pl ............ (2.102)
since S and Sl are both imaginaries, therefore C and F1 have to be zero for
equation 2.102 to hold. Thus there is no coml onent V of displacement
which shows there is no SH waves.
Rayleigh waves occur when one of the boundaries correspond to a
vacuum and we have a uniform half space. There is no SH wave. In the
absence of stress over the free surface, we equate the other components of
displacement to zero hence 2.100 becomes
{ a2 (I+?)- 2 p 2 ) ~ + 2~ 2~~ = o .............. (2.103)
and for stress 2.10 1 becomes
2rA+(l -s2 )B = o .............. (2.104)
From 2.103 we have
and from 2.104 we have
hence
using Equation 2.77 in which r and s are pure imaginaries with the
bracketed roots being less than one, hence factors under the bracketed
roots become real and positive. Using this 2.106 gives on
simplification
(2- c2l4 = 16 (1-c2 2)( (1-c2) .............. (2.107)
p2 a2 p2 2 2 on expansion and dividing through by C / P we obtain
The velocity c of Rayleigh wave cim be determined fiom 2.108 in its
relation with aand (3 . The equation has two real roots of C ~ h k h lies between zero
and f! under the codition that r and S are imaginaries. This be
found if we substitute the value C = f! and C = 0 on left hand side of
equation 2.108. Tnis type of surface wavz is pohrised with particles
of thz medium moving in vertical plane parallel to the direction of
wave motion. The velocity is less than that of bodily elastic waves in
the s k e medium. During the passage of Rayleigh waves, particles of
ground surface describe an ellipse in re trogade. It is refered to as
38
groundroll. Surface waves are suppressed during acquisition and
processing of seismic reflection data.
The seismic wave theory enables us to understand the
propagation and reflection of different types of seismic waves. This
leads to construction of ray paths geometrically to understand
reflection on plane horizontal and dipping surfaces.
2.3 Geonletrv of sesimic reflection ray Paths
2.3.1 In trodwction
In seismic method of data acquisition, the source wave field
propagates down into the subsurface. It is reflected at the geologic
boundaries. The reflected energy propagates back to the surface. It is then
recorded at the detector positions. The seismic response is determined by a
mixture of propagation and reflection effects. The propagation of primary
waves depends on the physical properties of the subsurface. The regection
depends on the local variations in the density. The subsurface information is
then derived from the reflection. The amount of energy reflected depends
partly on the angle of incidence of incoming wave field. In pre-stack
seismic inversion technique, determination of propagation free angle
dependent reflection is achieved. This information is lost on stacked data
(Berkhout 1987).
The use of geometrical optics is made here to relate arrival time to
offset distance. This is used in obtaining an expression for depth to the
reflecting interface.
' 2.3.2 Single horizontal reflector I
Fig.2.6a. Reflection from a s i n ~ l e horizontal reflector separatin~ two
lavers of inf6lnite thickness.
L Fig 2.65. Two layer medium with horizontal plane interface.
In the diagrams above AB represents the reflecting interface, S the
shot point, h is the depth to the reflecting interface, sc is the incident
wave and CR is the reflected wave. Also a, V, t and x represent angle
of incidence, average velocity, two-way travel time and offset
respectively.
It is easily seen that the following relations hold:
Hence
For the direct wave which forms the first arrival time t~ = x/v
............. (2.112)
The depth of the reflecting bed could be determined by measuring the
travel time (to) for geophone located at the shot point.
Thus at x = o, t = to.
Hence from equation 2.1 10
h = %Vto .......... (2.112)
Using 2.1 12 eqrmtion 2.1 10 becomes
Or t =x2+ to2 v2 .......... (2.113)
The ploting t2 against x2, we obtain a straight line graph with slope
1/v2 and intercept time t20.
To solve equation 2.1 10 for time, we use binomial expansion to
obtain
t = (3) [1+ (3) ] = to[l+l/? (3) - l@14+ ............ ] .......... (2.114) V 2h Vto 8 (Vto )
If tl , and t2 and XI, X2 are travel times and corresponding offset then
where At is the move-out. In a situation where geophone is coincident
with shot point, At is known as normal move-out (NMO).
At, = X .............. (2.116) 2v2to
This equation shows that the reflection curve increases rapidly
with offset but decreases progressively with increasing record time.
The value of normal move-out determines whether an event is a
reflection. When At, differs fiom the calculated value using 2.116 by
more than allowed experimental error, the event is not a reflection.
Dinping reflector. /
Fig. 2.7 Two laver ;medium with dipping interface.
The figure illustrates the geometry of seismic ray path for a
dipping horizon. The angle of dip is 8.
For a dipping plane interface equation 2.1 10 becomes
This gives us
Equation 2.118 is a hyperbola in which the axis of symmetry is
the line X = - 2hsin9 instead o f t axis as in a horizontal layer. This
shows that t has different values for geophones placed symmetrically
on opposite sides of the shot point. It is unlike the case of zero dip.
Setting X = o and 2h >> X in equation 2.1 17 and sloving for t, we
obtain
t = (1+x2 + 4h sine) % ............ (2.119) V 4 h2
Approximating only to the first term we have
t 4 to (1+x2 + 4 a i n e ) ........... (2.120) s h2
To find 8, we use hvo geophones on opposite sides of the shot
point with equal offsetsrm is for updip while + AX is for down dip.
tl and t2are corresponding travel times.
tl to [1+ (AX) + 4hAX sine ] ............. (2.121) 8h2
Ah =tl-t2~t~[1+(AX)2-4hd~sin0] 8h2
to ( s ) z 2AX sine h V
Sin0 = ?h VfAt8) ........... (2.122 Ax
The quantity V Atth is cal!ed dip movement. For small angle, hi 0 ;+: Sine and 0 is directly ?roportional to AtS. Also AtS is directly
propsrtional to AX for a given reflector. The largest LY allodfor is
used in accuiately determining the dip.
2.3.4 Several horizontal layers S+--- ----+R
1 Fig.2.tQRavpath ~eometrv for multilayered structure with several
horizonttll interfiices (Robinson and corugh 1955)
For a multi layered structure equation 2.11 3 becomes 2 2 ............. txp = X + t o.n (2.123)
V n m Where x is the offset and n is the layer of the reflector, V .,, is the
root mean velocity for the material from surface to the reflector and t t,,, is
the two-way vertical travel time to nth reflector. From fig. 2.8 it can be
shown that the following relations hold.
foPl = 2Atl v1
fo2 = a:-+ & = 2Atl +2At2 Vl v2
to,3 = 211-+ & 2h3 = 2Atl +2At2 + 2At3 ....... ( 2.126) v1 v2 v3
where b,l, fo2, to,3 are the two-way vertical travel time to the lst,
2nd and 3rd layers respectively and hl, h2 and h3 are the thickness of
each of the:e layers while V1,V2 and V3 are the average velocities of
the respective layers .
Atl, At2 and At3 are the one way increase in the travel time though the
respective layers.
We then use the root mean square velocity to analyse the travel time
along the offset path through the layers (Robinson and corugh 1988).
In fig. 2-18 the root mean square velocity V,, along the path SAR is
given by
for the path SDBER
The path SF H CIGR gives
Hence for n horizontal layers parallel to each other, the root
mean sq-uxe velocity along an offset path reilected at the nth
boundary is
A plot of arrival time versus effset obtained in a seismic section
enables us to determine the root means square velocity. The ms
velocities for reflection paths to n reflectors are calculated from the
slopes of hypenbolic travel time curves. ,
These velocities are then used with zero - offset time to find the
velocities and thicknesses of individual layers .in the structure.
Using equation 2.124
The vertical travel times Atl = to, 1 and At2 through these layers in terms of zero offset time is
At zero offset reflection i12 = i22 = i13 = iZ3 = i33 = 0 hence COS i12 = 1, then from equation 2.132 we have
........ v2, =[&LJ + v22 fb.2 &dl% (2.133)
to.3 - t o 2
hence
- h3 - V3(to.3- fo,2 )
2 for several n horizontal paralIel layers we have
and hn = Vn (kg - bpl)/2 ... ... ..... (2.140)
The determination of layer velocity and thickness is important
in seismic exploration. The sedimentary rocks of the subsurface are
layered, with different layers having different velocities, as a result of
density variation. The reflection time t, for reflections from nth
interface in a multi-layered horizontal structure is measured, then
using the layer velocities, depth to the interface is calculated.
47
CHAPTER THREE
DATA ACQUISITION IN SEISMTC REllECTION
PROSPECTING
3.1 Introduction
Seismic reflection data acquisition method is an application of
echo acoustics. The medium under investigation is illuminated fiom
the surface with acoustic waves. The incident wave field is reflected
at inhomogeneities in the medium. The reflected wave field is
registered at the surface. The detector records information on the
mechanical properties of the medium. This same principle is applied
in ultrasonic medical imaging and inspection of interior of materials
(Berkhout 1987).
In seismic reflection data acquisition the geologic subsurface is
illuminated from different positions on the surfrrce. The reflected
waves are optimally combined to maximinze signal to noise ratio.
T'nere is also optimization or" both vertical and horizontal resolution.
The field pocedures and operation principles of instruments
used in seismic reflection acquisition are described. The survey
methods are treated based cn their use on land and marine operations.
3.2 Can6 reflection survey
Land survey starts with the survey crew. The crew lays out the lines
to be shot and prepares the base map. Positions and elevations of shot points
and centres of geophone groups are determined. A geophone groups ranges
from three to hundreds connected in series or parallel. The output from each
geophone goes into the single amplifier whose output represents the average
ground motion over the group.
Holes are drilled at the shot points where charges are loaded by
drillers. Trucks, tractors or portable drilling equipment is used depending on
the terrain. To reduce groundroll holes are covered with sand after loading.
The recording unit connects seismic cable geophones in turn as
shooters move from one shot hole to the next to operate the blaster. The
recorders signals the shooters before a blast is released. When surface
energy is used, the source unit moves into place and the signal from the
recorder activates the sources to release energy into the shot point at a proper
time. A monitor record is made in the field either in parallel with recording
on magnetic tape or by play back on the magnetic tape. It is used to
determine weathering corrections and to check equipments.
In modern field procedures, holes where rnisfues occur are not
recorded or reshot. The use of comnon depth point (CDP) coverage has
reduced dependence on individual shot records. In CDP there is continuous
profiling because cables and shot points are arranged so that there is no gap
in the data.
1
k c tor
. Fig: 3.1 Common depth point profile
The CDP illustrated in fig 3.1 shows geophone groups evenly spaced
and numbered by their sequence along the seismic line. When shot A is
fired it gives a subsurface coverage from~f)ghahorizontal reflector. When
shot B is fxed it gives a subsurface coverage fiom b 6 hwhile shot c gives a
subsurface coverage from c to i. This process continues down the seismic
line. Each reflecting point is sampled more than once. The multiplicity
ranges fiom 6 to 24 fold. Many traces are recorded per reflecting point. A
reflecting point sampled 6 times has 600% or 6-fold recording hence six
seismic traces from that reflecting point.
When the bed is inclined, the depth point will be displaced up dip
from it's position midway between shot and receiver. The term common
midpoint (CMP) is used instead of CDP.
The traces from each reflecting point are then combined (stacked)
after removal of normal mow out in the subsequent data processing
operation. Stacking chaits are made to keep track of the many traces
involved. From the stacking charts, traces with the same shot poiat, same
offset, same depth point and same geophone are identified. Stacking charts
are useful in making static and dynamic corrections and to ensure that traces
are stacked properly.
The CDP technique is tlierefoie, designed to cancel noise of large
aparent wavelength such as groundroll, multiples and random noise
regardless of it's origin. This is because as with noise cancellation by means
of arrays, outputs of geophone groups distributed over a distance exceeding
a wavelength are summed.
Different types of spread ixe employed in seismic data acquisition.
The types of spread include split dip, end-on, in-line offset, Broad-L-spread,
cross spread, split dip spread with shot point gap and Broad side-T spread.
This is illustrated in figure 3.2.
(a) Split dip spread xxxxxxxxxxx xxxxxxxxxxxx 61
(b) Split-dip spread with shot point gap 1 12 13 24 XXXXXXXXXXXX (.) XXXXXXXXXXxx
1 24 (c) Brad-L-spread. Xxxxxxxxxxxxxxxxxxxxxxxx
(-1 1 24
(d) In-line off set spread. Xxxxxxxxxxxxxxxxxxxxxxxx (-1
1 24 (e) End-on spread xxxxxxxxxxxxxxxxxxxxxxxx (.)
I (.) W ( f ) Broadside-T spread xxxxxxvxxxxxxxxxxxxxxxxx r* X X x
(g) Cross spread xxxxx~~xxxxx I X
x 1%
. .
33 Fig 3.2 Types of reflection spread (Telford et a1 1976)
In split dip spread,shot point is located at the centre of a line
regularly spaced geophone groups. The disadvantage of this is that
when shot point is close to geophone, it gives rise to noisy trace. For
end-on spread, the shot point is located at the end of the line of active
geopho~e groups.
In Broad side-1 spread, the shot point is located at a point
normal to the cable at one end of active part while in broad side T, the
shot p0ir.t is opposite to the centre of the line of geophone group.
Both in-line and broad side offsets pepnit the recording of one to two
seconds of reflection energy before the groundroll energy arrives at
the spread. Cross spread consists of two lines of geophone groups
roughly placed at 90 degrees to each other and are used to record 3-D
dip information.
3.3 Land survey equinment
Land survey equipment can be classified under drilling, energy
source and recording. For dynamite source, holes are drilled with
rotary drills which are mounted on a truck bed or on a tractor or
amphibious vehicles. Hydraulic pumps are used in marshy areas.
Explosives are important seismic energy sources on land. Two
common types are gelatin dynamite and ammonium nitrate.
Dynamites introduces impulsive seismic signal into the earth. The
amount of dynamite needed for reflection shot varies from less than
2kg to se-/era1 hundred kilograms. This depends on the lithologic
characteristics of the geolgogic section below the shot and the depth
of penetration desired. It's drawback is the cost of drilling holes and
danger to human health. The efficiency of energy transmission
depends on the material, it's moisture content, charge size, hole depth
etc.
Vibrating sources are used to put signals which persist for many
seconds into the earth. An example is vibroseis. Energy is introduced
into the earth over the entire range of seismic frequencies. The
efficiency of the transmission depends on the nature of the subsurface
material. The mzin disadvantage is that the frequency content of the
signal introduced into the earth is not subject to control . Weight
dropping acd land air gun are otiier non dynamite sources which are
used.
Vibroseis data posses a certain noise known as harmonic ghosting by
which a vibrator earth system introduces a frequency that is twice the
fundermental frequency being sent out.
The main instrument used in detection and recording of seismic
energy is the geophone. The other recording equipments include
amplifiers, tape recorders, and computers. The entire recording
process in the field is controlled using computers. I t is also used in
monitoring field operations. The computer is also used for work
station processing and interpretation of 3-D data. The geophone is in
direct contact with the earth it detects aid converts ground motion
into electric signals. The modern geophone is an electromagnetic
instrument. The voltage generated in the geophone is directly
proportional to the velocity of ground motion.
According to sheriff and Geldar-t ( 1 983), a geophone coil in
motion is acted upon by three forces. These are restoring force of the
springs, the force of interaction between the permanent lnag~letic field
and the magnetic field of curfent and the frictional force.
Using Newton's second law of motion, we have that
where x is displacement of the surface and geophone,' x, is
displacement ol'geophone coil relative to permanent, magnet I current
in the coil, z is the mechanical damping factor, s is spring constant, f
is force stretching spring through distance Ax, m is mass, r is radius
and n is number of turns of coil whilc ki is force on coil due to
current, R is resistance, L is inductance.
................. K = 2 n m H (3 3
e.m,f induced in the coil = - d$ /dt (d$ /dxc) (dt)
Differentiating 3.1 and substituting for d ~ J d t the geophone equation of motion becomes.
For a geophone output to be independent of frequency, L must be
equal to zero. However L is a assumed to be negligibly small hence
where dildt represents damping. At zero damping, system becomes
simple harmonic with natural frequency V, given by 'h
Vo=!& = (l) (s3 ............. 27~ 27t m (3 3
with damping we have
............. where Zho, = (dm + K ~ I ~ R ) , h (3.9)
being damping factor.
Equation 3.8 is for damped motion. To get the transient solution, we
set the right side equal to zero.
Assi~ming i=o, di/ dt = IJo al t = o. l ' l ~ e ~ i the soli~tiol~ l~ecomes
for Ii > I (over- clamped)
for 11 = I (critically da~nped) i = Uo/ exp-( {r.o,t)
'I'llcsc: sollllions :IIT I rn~lsic~ll 1)ccarw i avc~lt r~;~lly Oecon~es zero d i~c to
I'or praclical pilrposes [lie geoplio~ie se~lsilivity is, tlcter~nined~
largely by k 11, this iii~plies se~isitivity depe~ids on radius,
nu~l~ber ofttllhs of coil, niagnetic field slrengtli and dampine. 1 11~0.3
Fig.
fiwtor (sheriff and Gcldeart 1983) ' '
These solutions are sllow~l i n fig. 3 ill t e rm of resoliant period TO for
clifl'erenl tlanlping factors 11. For 11 > I, the currellt starts to build up
becar~sc of the sidi faclos, but the11 decreases as the exponential factor
begins to dominate. When 11 < I , llle outpi~t is a clamped sine wave
aid successive peaks occiu at i~~tervals. For 11 - I , the critically
damped case, the output just Sails to be oscillatory.
2 I \ '1'0 =27~/{(00(l-h ) , . . . . . . . . . . . . . . . (3.13)
and ratio of the successive peaks is 2 H iJin +1= exp [2nh (1- h ) ]
where
6 = In(in/in+l-) =21~h(l-h2)"
By measuring 6, h can be obtained when h < 1. To obtain the
geophone response to a driving force, assume that it is subjected to a
harmonic displacement such that the velocity dddt = Vo cosot, then
X = (Volw) sinwt,
d2X/dt2 = - ~ V O sinot, d3x/dt3 =-02Vo cosot.
hence equation 3.8 becomes
d2 i/ dt? + 2hqdiI dt +&t = (-a2 KVOIR) cosot . . . . . . . . . .. (3.15)
The solution of equation 3.13 has two parts. The transient solution is
given by equation 3.12 to 3.14. The second is the solution
representing the forced motion of the geophone resulting from motion
of the ground.
i= (Volz) cos (o t+y) 2 'A where z = @w2kw2) [{ 1 -(w/wo )2}2 + (2ha2/+w0) ] . . . . . . . (3.16)
tany = (2wh/oo) { ( o ~ w , ) ~ - 1) ... ... . (3.17)
Thus the amplitude of i for a given geophone depends on Vo,. o/oo
R, k anC h. When o + a, z -+ R/K and the amplitude of i
becomes i, = Vo KR.
One of the most important characteristics of a geophone is
output voltage per unit velocity of the case. The sensitivity called
geophone transudation constant r is defined by
r = amplitude of output voltage 1 amplitude of geophone velocity
Assuming the geophone is connected to an amplifier with an
infinite input impedance, the output voltage is the voltage across Rs,
which is the shunt resistance. Using equations 3.6 and 3.12 we get
r = Rs(Vo1z)No = Rslz
= K(Rs/R) F(o1oJ
where F (olo,) = o when o = o
= 1 wheno=oo
= %h when o = o,
For practical purposes the geophone sensitivity is determined
largely by K and h, This implies that sensitivity depends on radius and
number of turns of coil, magnetic field strength and damping.
The signals from geophone groups are fed into an amplifier.
This amplifies weak signals. Also signals are compressed to useful
range of amplitudes. The goephone outputs are also filtered to
enhance signal to noise ratio. There are digital and analogue
amplifiers. Seismic signals are generated and recorded in analogue
form beforc Cigitization. In analogue, signal is expressed as a
continous function respresenting the amplitude of the signal as a
function of an independent variable w i c h is often time. Continuous
signal is registered on a magnetic tape having a magnetization
continuously varying along the tape. Modem recording is either by
frequency modulated or pulse- width modulation technique . In
frequency modulation (F.M.), amplitude of output from the amplifier
modulates the frequency of a 3000HZ carrier signal over the seismic
range (10 to 300HZ). Signal is extracted upon play back by
demodulation. In p$e-w& or amplitude modulation (AM), the
signal is impressed directedly upon the tape the magnetization of the
tape is proportional to the strength of the signal up to the limit of the
tape's dynamic range.
In digital recording, the signals from each detector group are
fed into an amplifier (one for each group) using binary gain amplifier,
in which the gain changes in steps of a factor two. The recorded data
is then multiplexed, wliicli converts signal magnitude into a binary
number transcribed onto a magnetic tape. A binary sequence is
obtained after multiplexing and digitization. Sampling is done in the
sample and hold unit. The output from this unit goes into analogue to
digital converter. Tlie signal wliicli emerges is in the form of pulses
having uniform height, The signal passes througli the buffer and
format controller before it is recorded on digital tape.
3.4 Marine reflection survey.
Marine reflection survey is carried out on water, the water
being deeper than about 10m and needing sizable ships, about 50111 in
length. Some land acquisition techniques are applicable to marine
survey. The use of multiple receivers and CDP tecliniqrre is
applicable to marine seismic survey.
In marine exploration, the energy sources introduce a sudden
positive (or sometimes negative) pressure impulses into the water.
The imprllse involves a compression (or rarefaction) of water
particles, creating a sliock wave that spreads out spherically into the
water and then into the earth. When the sliock wave is delayed, there
is an oscillatory flow of water in tlre area around the explosion. This
causes srlbsequent pressure pulses designated as bubble oscillation.
Tlie bubble oscillation determines the properties of the seismic signal
generated by all marine energy sources.
The most widely used energy source in marine survey is the
airgun. This discharges highly compressed air into the water. The
impulsive sources (liydroseis, flexichoc) may be said to be the
converse of the airguns. These initiate a pulse when the hydrostatic
pressure of external water makes the walls of an adjustable evacuated
chamber to collapse on sudden removal of the restraint keeping the
walls apart.
The detectors for marine work are called hydrophones or
pressure phones. They are used 61- detecting seismic signals in
appreciable depth of water. They utilize the phenomenon of
piezoelectricity. This is based on the fact that certain materials
develop electrical charges. When subjected to mechanical stress. The
voltage generated is proportional to the instantaneous water pressure
associated with seismic signal. The pressure is proportional to the
velocity of tlie water particles set into motion by the signal.
The material used in hydrophones is mainly barium titanate. It
is either in disc or hollow cylindrical form. Tlie cylinder form is
closed at both ends with brass caps. When subjected to bending due
to a pressure wave, the outside and inside of the hollow cylinder will
become oppositely charged. The voltage between the surfaces is the
output of the liydroplione which is proportional to the velocity of the
surface. Each hydropone consists of up to 50 series of coupled
elements. Special waterproof cases are designed to permit planting of
moving coil hydropl~ones in marshy ground.
Tlie hydrophones are contained in a tube several kilometers
long, called streamer. The streamer is reeled off and positioned in tlie
water astern- a ship, while the ship is still arriving in the area of work.
This is followed by the seismic source units; shots are fired and
recordings made w h i k the ship is moving.
This is necessary as otherwise the trailing streamer cannot be
kept in position. Detailed monitoring of data quality is not possible
because of the ship's motion. Work proceeds generally on a 24 hour
basis but not all time can be spent shooting. A major problem in
marine operation is to know the ship's position at any instant. Nearly
all energy sources in common use are towed at a distance far enough
from the stern of ship to avoid the possibility of damage to the ship's
hull. The distance between the source and nearest receiver group is
about 30m.
Drifting away (feathering) of cables fiom the line of motion of
the ship and position of hydrophones occur due to cross currents.
This causes detoriation of data in CDP stacking. The tail bouy is
difficult to see but it is designed to be observable on radar screen.
The tail bouy contains a light for visibility atuight so that it's position
will always be known.
3.5 3-d reflection survey rlesim and data acqoisitim
The main aim of 3-D survey is to obtain a three dimensional
migrated wave field. The success of the migration depends on the
stack-quality as well as the accuracy in velocity estimation. The
subsurface is real 3-D, the more complex the subsurface is the greater
the need for 3-D exploration. Better imaging of the subsurfBce can
only be achieved by higher dimension survey and migration. In
moderate complexity of subsurface, 2-D migration is inadequate 3-D
survey is important because migration requires adequate spatial
sampling of the seismic wave field.
3-D surveys are canied out in such a way that the data to be migrated
are obtained in a 3-D volume with closely spaced traces in both in-line
and cross line directions. The detailed overage provides a more
detailed and reliable interpretation.
Land 3- D surveys are commonly acquired with the swath
shooting techniques. In this, the receiver cables are laid out in
parallel lines and shots are positioned in perpendicular direction. The
line spacing in 3-D survey may be 50m unlike 2D which may be
Z O h . The dense coverage in 3-D requires a good knowledge of shot
and receiver location. This shooting pattern provides a wide r a n g of
azimuthal coverage, which is important during velocity analysis.
Swath shooting is economical. The receiver cable sections are moved
up from the rear of the swath to the forward end while shooting
continues. Once one swath is completed, another one parallel to it is
recorded and this procedure is repezted over the entire survey area. It
is usehl in- the entire survey area. It is useful where there is
environmental or topographic restriction. Coverage over a
topographic high can be achieved by shooting vound it. A complete
loop is made with shots and receivers located on the loop.
The size of th2 survey area is not only dictated by the ,*--,-
extent of the target zone in the subsurface, but also by the aperture
size required for adequate migration of the 3-D seismic data volume.
This inctecses the arreal extent of a 3-D seismic survey.
A cell is a rectangular area on the earth's surface and constitutes
the basic element of a grid that covers the entire area of the 3-D
survey. A common-cell gather coincides with the CMP gathers for
swath shooting.
Typical size of a cell is 25x25m for land surveys and
12.5x37.5m for marine surveys. The gathers are used in velocity
analysis and the cell stacks are generated.
A marine 3-D survey involves shooting a number of closely
spaced, parallel 2-D lines (line shooting). In the shallow water
environment, the swath shooting technique for land acquisition is
preferred. The direction in which the ship sails is called in line
direction, the direction perpendicular to it is called cross line. The
receiver cable is subjected to a certain amount of side ways drift
(feathering) from the ideal streamer line due to cross currents. This
causes problem of travel time deviation from a hyperbolic move out
within a common cell gather in 3-D surveys especially where there is
a dipping a event.
The common practice in marine 3-D shooting is to use two ships.
Each ship is equipped with both a source array and a recording cable.
The two ships travel abreast a few hundred meters apart. The two
ships alternate firing their source arrays. In the simplest configuration
for such bvo ship operation, three subsurface profiles are recorded
during the traverse of a line . Subsurface coverage produced by each
ship would be one and one-half times as much as that obtained by the
one ship acting alone. The use of two ships reduces the cost of the
survey.
CHAPTER FOUR
PROCESSING AND INTERPRETATION OF SEISMIC
REFLECTION DATA
4.1 Introduction
The analysis of acoustic waves reflected fiom different rock
layers in the earth's subsurface is the objective of exploration
seismology.
The acquired data is analyzed to obtain information on the
subsurface despite it's complexity. This could have been easy if the
wave suffers only reflection while passing through the earth and it
occurs only on the surface of the geologic boundary. However the
incident wave is affected by absorption, high stress near the shot, peg
leg multiples, diffraction and sequence of reflections from various
layers. 'l3e result is that the reflected wave received has to be
processed to obtain the primary reflection.
Generally the information that c m be obtained from reflection
depends on, (a) The propagation properties of absorption and average
velocity (b) The reflectivity properties of density and elastic moduli.
In each geologically related layer, the average velocity parameters and
the reflecting boundaries have to be delineated. The information
obtained must be clear and precise to give reliable interpretation.
4.2 D:~ta ~ r o c e s s i ~
The data obtained from the field is taken to the processing
centre. At the processing centre the appropriate time shift is made to
correct for static and dynamic variables. Filtering is done to enhance
signal to noise ratio. Using velocity estimates, velocity analysis is
carried out and the stacked sections are produced. The data is
migrated for repositioning in order to align with the position in the
subsurface. The processing stages involves use of signal theory and
mathematical formulations. These are used in obtaining the time
shifts to produce time seismic sections.
The various mathematical theories and stages of processing
include, Fourier transformation, convolution and correlation.
4.2.1 Fourier transformation
The data presented in seismic section can be viewed in two
ways. In one way we study the variation of amplitude of output with
time, in this case we are operating in time domain. The same seismic
record can be viewed as the superposition of many sinusoidal waves
of differing frequency and this corresponds to the fi-equency domain
(sheriff and Geldart 1953).
A function can be transformed fi-om frequency to times domain. Also
the inverse transform can be carried out.
Tlle Fourier series representation of a well behaved function g
(t) of period t is given by
g (t) = C a. Pvnt
where
in the limit of T infinite, we have
a3
g (t) = G (~)ej '"~ ' dv - 00
CO
or G (v) = 1 g (b)ee2KVt dt ............. - CO
(4.4)
The h c t i o n G(v) is Fourier transform of g(t).
Q(t) is in verse transform of G(v)
9 0 ) ct G W
Generally
G(v) =
Hence
g ( 0 =
where
CO
1 A (v) cos [ 2xvt + y(v) ] dv, .... (4.6) - CO
A (v) represe~ts the amplitude spectrum while y(v) represents
the phase spectrum.
a3
R(v) = 1 g(t) cos2xvt dt ......... (4.8) - a3 a3
- x ( v ) = j g ( t ) ~ i n h v t d t .......... (4.9) - c0
X(v) and - X(v) are the cosine and sine transforms respectively.
4.2.2 Convdu t : o ~
Is a time domain operation in which each element of an input
function is replaced with an output function scaled according to
magnitude of input element. The outputs are then superimposed.
Considering a linear system, the output of data sampled at
regular intervals can be calculated if we know the impulse response.
Using 6t as impulse response of discrete data and 6 (t ) as impulse
response of a continuadata, and for successive sampling intervals.
6t - I System f t = [ % , f l , f l ..... J
at t = n, unit impulse, we have
kdt __+ System ____+
............. (4.11)
For series of sampled values, the input can be represented by unit
impulses multiplied by appropriate amplitude factor.
..... Let& = [f = [f,,f 1, f ] be the impulse response of o~ tpu t filter.
and
gt .... - - [g,,gl, g 2 I.. .be the input response.
ht = f i * g t = 5:fk g(.k = Z g l r f t l
for two continuous functions
00
h(t) = f ( t )*g( t )= l f ( r g ( t - r ) d r ............. (4.13) -00
The convolution theorem states that the fourier transform of the
convolution of two functions is equal to the product of the transform
of individual functions.
pt ++F (v) = lF(v) 1 e jy ' (") ............ (4.14)
gt c * ~ l ( v ) = IG(v) ejyg (") ............ (4.15)
............ Ft 'gt - IF($ k ( v ) h J { yf(v)+yg(v) I (4.16)
F (v) and G (v) are amplitude spectra while yf (v) are the phase
spectra
Convolving two sets of data in time domain gives an effect in
frequency domain. The effect is the multiplication of their amplitude
spectra and addition of the phase spectra by symmetry.
........... ft gt - F (v) * G (v) (4.17)
Convolution principle is applied in sampling and aliasing. In
and log-to digital conversion continuous signal is replaced with
discrete values. The wave form on seismic record is a result of
successive convolutions of shot impulse with impulse resgonse of
various layers of the earth.
Deconvolution is a process of convolving with inverse filter.
ft * it = & where i t is the filter and ft is the inverse filter.
Deconvolction is used in removing singing effect of water in marine
survey. The propagated and reflected seismic waves undergo
convolution with the earth in various ways. Xn deconvohtion these
effects are removed during data processing.
4.2.3 Correlation
It is a measure of similarity between two different sets of data.
Let Xt and Yt be two sets of data
............ 4.y ( ~ ) = C X tr YkfT (4.18)
r = displacement of Yt relative to Xt . If 4 , (r) has large negative
value, there will be similarity if one set of data is inverted.
one data set is reversed, then convolved with the other set of data.
X, o X(v) = I x (v) le jv ............ (4.20)
~ ( 3 o Y(V) = I ~ ( v ) le jw ............ (4.21
X- , o X(v) = 1 x (v) le jv ............ (4.22)
$xy (T) ff X(y) y(v) = k(v) I k(v) le ' [v(x) - ~ ( v ) 1 ..... (4.23)
Cross correction in time domain gives in the frequency domain
an effect which is same as multiplying the complex spectrum of
second data by conjugate of the complex spectrum of the first set.
Forming the complex conjugate involves only reversing the sign of
the phase, hence cross correlation is equivalent to muiltipying the
amplitude spectra and subtracting the phase spectra.
Auto correlation. In this case one set of the data is corrected with
itself. It is a measure of repetitiveness of a function.
Auto correlation has it's peak value at zero time shift. If auto
correlation has large value at some time shift not equal to zero, it
indicates the set tends to be periodic with At. For continuous
functions in cross correlation.
a
............. oxy ( 3 = I X ( 0 Y (t+r) dt (4.25) - a3
for auto correlation it be becomes a3
4 (T) = x (t) x ( t + ~ ) dt ............. (4.26) - CO
At zero shift, auto correlation value is called the energy of the trace.
@a (0) = E X; . . . . . . . . . . . . (4.27) k
Correlation functions are applied in processing of reflection data. In
vibroseis. It is also used in sign-bit recording and ~nultichannel
coherence.
4.3 Processing sequence
The use of digital recording and computer processing has
introduced a routine sequence in processing of seismic data. Primary
stages of data processing are filtering, deconvolution, velocity
analysis, stacking and migration, secondary processes are applied at
each stage and that depends on the processing centre.
4.3.1 Filtering
Frequency filtering is carried ortt to attenuate noise whose
frequencies fall outside the signal range. It improves record quality.
Velocity filtering is used in removing organised noise particularly
groundroll from shot record. It can also be performed on Pecords
sorted into shot gather, receiver domain and common midpoint gather
respectively. Filtering in shot domain is preferred using f-k because
signal and noise are separated.
4.3.2 Demultiplexing
Field data is recorded in tnultiplexed mode. It is demultiplexed
in the processing centre. The data is sorted into columns of samples.
The samples i n one column are followed by those in other channels.
Demultiplexing is seen as transposing a big matrix. The columns of
the resulting matrix can be used read as seismic traces recorded at
different offsets from a common shot point. This can then be used for
resampling.
Trace editing
This is the removal or correction of any trace record which in
it's originally recorded form may cause detoriation of the stack. These
include dead trace and strong noise out bursts
Gain recovery.
It is a time variant scaling. This is applied on the data to correct
amplitude effects of wavefront divergence. The amplitude of deep
reflections may be so small that it may not be recognised on the
record. The applied coi-rections compensate for geometric spreading,
absorption and transmission losses. Gain functions are applied at
various stages of processing to bring up weak reflections.
4.3.3 Field static corrections.
It reduces the travel times of the various shot point to a
common datum level. It is used in removing near surface effects. The
two corrections applied are weathering and elevation corrections.
Weathering correction is applied to compensate for changes
along the seismic line on raw reflection time. It arises fi-om variation
in thickness and velocity of the weathered layer.
W, = Weathering correction where d, is the thickness of the
weathered layer, V, is the weathering velocity and V, is the correction
velocity.
Elevation correction is applied to correct topographic effect on raw
reflection time due to elevation of seismic sources and receivers on
the surface. El< = elevation of receiver,
E,s = ED-E, v c
Where En is dutum elevation from sea level, Es is source elevation
from sea level and E, is elevation correction. Field statics correction
is the algebraic sum of weathering and elevation corrections. If t,, is
the field statics time and trrIr is the upliole t h e .
.......... tl)=EcS+Ecl<- t r ~ r 1 = 2 E d - @ , + E ~ ) - - ~ I I I I (4.31)
v, 4.3.4 Deconvolution.
Deconvolution is used in removing filtering effect introduced
by the earth during propagation of tlic wave. The effective source
wavelets contained in the seismic trace are compressed to a spike.
The ideal is that the output h(t) is known and we are to recover the
form of the input signal f(t) before it was modified by the filter.
Suppose the filter response is K(t) a~ld h(t) is passed through it to
recover f(t). K(t) in this case is an inverse filter with respect to
impulse response g(t). The filter response is then cancelled with
another filter. The time domain equation is given by
F(t) = h(t) * L= I#) * K(t) ......... (4.32)
While in the frequency domain it is . . . . . . . . . . (4.33)
F(h), H(n), G(n) and K(n) are frequency spectra of Fourier
transform of the respective Rf), h(t)8$ld K(t) respectively. In
deconvolution long initial wave form of a marine source can be
transformed into a shot wavelet. Land data have an initial short wave
form consisting of shot pulse which is broadened by filtering action of
the earth. Deconvolution brings back the waveform to it's nature
before filtering by the earth.
4.3.5 Common midpoint sortinv.
The purpose of common midpoint (CMP) sorting is to improve
signal to noise ratio by attenuating random noise (sengbush 1953). It
is assumed that the reflection signal on the traces of a CMI) gather are
identical and the random noise is mut.~ally uncorrelated from trace to
trace. The data is transferred from shot receiver cooordinate to
midpoint offset co-ordinate. The three co-ordinates in which
conventional 2-D data exist in space xe time, offset and x co-ordinate
along line of profiling. In stacking, offset co-ordinate is compressed
to zero along midpoint axis. This then gives the CMP sorting. The
traces with same midpoint are grouped together to obtain a CM?
gather. In a horizontal reflector in a dipping reflector they are
different.
4.3.6 Ve!ccity a ~nlvsis/Nrno correction
Normal moveout (NMO) correction is a dynamic correction. It arises
from increase in offset as detector positions are moved farther away
from the source. The initial velocity analysis involves calculation of
normal moveout velocity from measurements of normal moveout
(sheriff 1984). The NMO velocity is the velocity of a constant
homogenous isotropic layer above a reflector which would give
approximately the same offset dependence as actually observed. This
is the value determined in velocity analysis. It is applied to remove
the influence of offset on travel time. The NMO velocity is based on
the small spread hyperbolic travel time. Stacking velocity is based on
the hyperbola that best fit data over the entire spread length. 2
The travel tx time as a function of offset is given by ex = e0 + /v2
At = tx - t,, = (& + 6 V 2 f%- &,where t,, is time at zero offset, At is
moveout, X is offset, V is velocity. These are equations of hyperbolic
trajectory used in velocity analysis.
Application of NMO correction virtually flatten all events
across offset range. Traces are stretched in a time-varying manner
causing a shift in frequency content. This is because it is a dynamic
correction. This mainly affects shallow events and larger offsets.
AElf = Atmd t,,
where f is the dominant fiequency, t, is the vertical travel time at shot- point, X is the offset and V is velocity.
4.3.7 Stnckin~.
Common midpoint stacking is carried out by summing the
events over the offset. It is the combination of two or more traces
together. It is done in different ways depending on the purpose of
stac!&g. Stacking can be used to test NMO correction and to
determine velocities in the subsurface. It can be used to reduce the
amount of processing job by combing adjacent traces.
Traces are normalised after stacking especially in CDP gather, in
which it is divided by the number of traces. In CDP stack the
difference in geometries of primary and ~nultiple reflections is used to
weaken multiples.
4.3.8 Residual static correction
The assumption made during static correction is that tlie travel
path from datum to receiver is vertical. This is not always true. Also
if the crew uses surface sources, only approximate weathering
corrections can be made. This introduces a series of small,
unsystematic errors in the original field static corrections. These
errors are called residual statics.
This correction is applied to the N MO-corrected CMP gathers.
I t is done in a consistent manner on shot-receiver locations (Yilmaz
1987). Tlie estimated residual statics are then applied to tlie original
CMP gathers. It is done in a consistent manner in wliich time shifts
are dependent only on shot-received locations (Yilmaz 1987). Tlie
final stacking is done using improved velocity field.
4.3.9 Migration
Migratiotl is data positioning ad-justment. It moves energy from
it's CMP position to it's proper spatial location. The aim is to make
the stacked section appear similar to tlie geologic cross-section along
seismic line. 111 migration a depth section sliould be obtained from a
stacked section, however in accuracy of velocity estimates makes
stacked sections to be displayed in time. Migration collapses
diffi-actions to focii, increases visual spatial resolution, corrects
amplitude for geometric focusing effects, spatial smearing and moves
dipping events to their true (supposedly) subsurface location,. I t is
regarded as imaging process. The three main types of migration are
kirclioff
summation, finite difference method and Fourier transformation
method. Kirchoff summation combines data found along curves on
the section. Finite difference migrates data layer by layer, while
Fourier transform migrates data which is expressed in terms of
frequency and wave number. Time section migration is appropriate
since lateral velocity variations ;rre moderate.
Migrated seismic sections are used for geologic interpretation.
4.4 Tnterpretation of seismic reflection 'data.
4.4.1 Introduction
The objective of seismic survey and interpretation is to locate
structures which prove excellent hydrocarbon traps. The lithology
and geologic history of the area is derived to form an opinion on the
probability of encountering petroleum in the structures mapped.
Icterpretation of seismic data is the translation of the
information obtained by the reflected acoustic energy into the geology
of the subsurface. It is important to understand the geologic factors
that generate reflection. The orgmic materials which form crude oil
are buried to a depth where temperature and pressure are high enough
for conversion to petroleum .
Petroleum is found in a rock layer. The porosity of the rock
influences the quantity of oil contained in the total volume. Petroleum
is found in a porous rock layer but there must be sealing rock layers
below and above the porous layer which traps the oil. The oil is
prevented by the seal from migrating to the surface.
The information to be extracted for interpretation of the
geology of an area are structural traps, lithology and stratigraphy of
the subsurface (Brown and fisher 1982). These are obtained using
seismic method and are used for evaluation of the subsurface.
Interpretation starts with assembling of the data as tools for
interpretation. These include seismic sections, well log data, velocity-
depth profiles, vertical seismic profiles, synthetic seismogram, other
geophysical data and paleontology studies. The knowledge of
regional geology of the area is vital to obtain a consistent
interpretation.
According to sheriff and Geldart(1983), the interpretation of
seismic reflection data is based on these geophysical assumptions.
The coherent events seen on the seismic records are reflections
from acoustic impedance contrast in the earth.
The acoustic impedance contrasts are associated with bedding which
represent geologic structures.
Mapping the arrival times of coherent events gives the map
showing the geologic structure. The seismic-wave shape ax!
amplitude are related to geologic detail hence reveal the stratigraphy
and nature of the interstitial fluids.
4.4.2 Ch:~ractc?rktics of seismic e-ients.
T ~ P characteristics of seismic events hzlps us to select events
which represent primary reflections. To interpret seismic section, we
pick the strong reflections then obtained arrival time for mapping of
the reflecting horizoas. The following features distinguish events in
the seismic section.
Coherence. This refers to the similarity in appearance fiom trace to
trace of peaks and troughs. The wave produces the same effect on
each geophone hence the wave shape looks more or less alike for
strong events during the interval it arrives at the geophone.
Amplitude standout refers to the increase of amplitude that
results from arrival of coherent events. Coherence and amplitude
standout tells us if the event present is strong or weak. In a seismic
section, the alignment of peaks and troughs represents a layer where
there is strong seismic event resulting from contrast in acoustic
impedance. Character refers to the distinct appearance of the wave
form. It is used in identifying a particular event, for instance event
may be a diffraction or a reflection.
Moveout is the systematic difference in arrival time from trace
to trace of an event. It is the most distinctive criterion for identifying
events. Character and normal moveout are used in identifying the
type of event. Diffractions and refractions have higher normal
moveout than primary reflections. There is a range of normal
moveout for which an event is acceptable as primary reflection.
The presence of oil may cause significant change in reflection
character. Interference may occur also phase reversals take place at
the edges of reservoirs,. There is a spiit of wavelets at the fault
termination. Also gas reservoirs cause high absorption of seismic
znergy. The .howledge of characteristics of seismic events is
important in interpretation of seismic data. It is also important to
know the structural styles and stratigraphic patterns which produce
special characters on seisnic sent' ions.
4.4.3 Hydrocarbon habitats and trap pin^.
Hydrocarbons are trapped due to different tectonic setting and
stratigraphic patterns. In this section we examine various structures
that trap hydrocarbons.
Faults and rock deformation.
Faults are produced by unbalanced stresses which exceed the
strength of rocks. The type of fault depnds mainly on which
component of the stress is greater. Normal faults result when the
maximum compressive stress is vertical and the minimum
compressive stress is horizontal. The dip is of the order 50 to 60
degrees. Reverse faults or thrusts occur when the maximum
compressive stress is horizontal with a fau!t plane dip of order 30 to
40 degrees. When the maximum and minimum stresses are
horizontal, wrench faults occur with angle of about 30" to the
minimum stress direction.
Anticlines, synclines and domes may result when the rock
folds under stress. Anticlines are produced whzn the fold is upwards.
Syncline are produced when the fold is downwards. Domes result
when solid structures of various shapes p ro~ube upwards.
Deformation which creates structures capable of trapping
petroleum is relatively cold defoim~tion. i t tzkes place under
temperature and presswe condit ic ns which are mild. "Cold"
deformation implies that associated fractures propagate in generally
elastically deforming media. According to Bally (1975) this follows
shear failure.
Faults are good oil and gas traps. In most cases the permeable
beds overlain by impermeable bed is faulted against the impermeable
bed. A trip exists if there is a closure in a direction parallel to h e
fault as when there is folding. Hydrocarbons are mainly trapped
upthrown to normal faults. Downthrown faults exist mainly when the
normal fault is associated with rollover anticlines and are listric faults
(Tearpock and Biscke 1991).
The extensional tectonic habitat is one of the principal
petroleum related settings for normal faults. It is a major large scale
gravity slide structure. The normal faults in this category decrease in
dip with depth to low angle fault. The often become bedding plane.
The major listric fault is refereed0 to as master fault. These listric
growth faults are syndepositional. The exhibit significant increase in
stratigraphic thickening in the down thrown block or hanging wall.
This type of stratigraphic thickning indicate movement along the
surface of the fault during deposition. These faults are
contemporaneous because it was occurring when adjacent sediments
were being deposited.
According to supper et a1 (1984) growth faults are often
associated with anticlines called rollovers. There develop as a result
of bedding on the handing wall fault block. The rollover anticlines
are important hydrocarbon traps associated with listric growth faults.
Hydrocarbo accumul~tion is expected to occur at the crest. The
structural style of Niger delta is dominated by growth faults with
associated rollover anticlines.
Wrench faults are high angle vertical strike-slip faults. They
from under horizontal compression. The primary hydrocarbon traps
associated with wrench faults are anticlines that saddle the wrench
system. The faulting may be normal or reverse. Wrench faults are
good hydrocarbon traps because they form early and coininonly
develop large closures.
The compressional tectonic settings are good hydrocarbon
traps. The hydrocarbon is mainly trapped by hanging wall anticlines.
It might be a fault propagated fold, fault bend fold or duplex
structures. Synelines are not good traps as the hydrocarbon migrates
from the sides (Hindle 199 1). Intrusive salt structures have extremely
varied and complex geometry resulting in numerous types of
hydrocarbon traps. They include simple domal anticlines, graben
fault traps over the dome, porous cap rock (limestone or dolomite),
flanks or pinchouts, traps beneath on overhang, traps against the salt,
unconformities, fault traps down thrown away from the dome and
traps towards the dome.
Unconformities alone or in combination with faults or
stratigatpliic anomalies such as sand pinchouts series as excellent
hydrocarbon traps. An unconformity is a surface of erosion or non
deposition that separates strata of different ages. It's development
involves several stages of activity. The initial sediment is deposited,
then subaerial erosion or non deposition takes place hence there will
be a deposition of younger sediments above the unconformity. They
exist in many geologic setting but occur mainly in steeply dipping
structures. The nature of sediments above and below the
irnconformity are not parallel to one another. The rocks below dip at a
steeper angle than those above. Impedance contrasts occur hence
unconforrnities are good reflection.
Stratigraphic traps.
Stratigraphic concepts are important in the study of seismic data
(Brown and fisher 1982). A classification of stratigraphic traps is
given by sheriff and Geldart (1983) as modification of the table of
stratigraphic traps from Rettehouse (1972). The classification is used
below to show various types of stratigraphic traps.
Classification of strntigrnvhic
Not adjacent to unconformities.
facies-change traps involving current transported reservoir rock.
Folian (dunes and sheets)
Alluvial fan
Alluvial valley (braided stream, channel fill, paint bar)
Deltaic (distributary mouth or finger bar, spit, tidal delta or flat)
Non-deltaic coastnl (Seach, barrier b:u; spit, tidal delta or flat)
Shallow marine (tidal bar, sand belt, washover, shelf edge,
shallow turbiditc or wimowing).
Deep marine (marine fan, deep turbidite or winnowing)
Non current transported reservoir rock
Gravity (slump)
Biogenic carbonate (shelf-margin reef, patch reec algal build-
up or blanket)
Diagenetic traps
Change from Non reservoir to reservoir.
Replacement and leached (dolomitized
Leached
(Brecciated)
fractured
Change from reservoir to non-reservoir
Compaction (physical or chemical)
Cementation
Adjacent to unconfomities.
Traps below unconformities
seals above uncornformities
subcrop at unconformities
Topography (valley flank or shoulder, dip-slopes escarpment,
valley, beveled).
Seal below unconformity
mineral cement
Tar seal
Weathering product
Traps above unconformity
Reservoir location controlled by unconformity topography
on two sides (valleys, canyon, fill)
on one side ( M e or coastal cliff, va!ley side).
Transgressive.
4.4.4 Evidence of fmd:'nz on seismic sec~on .
The fallowing are evidences of faulting on a seismic section (sheriff
1952).
(1) The abrupt ternination of reflections especially on migated
data.
(2) Sharp change in amplitude caused by diffraction to a fault
termination.
(3) Changes in actual dip associated with the fault which may
flatten or deepen depending on the nature of the fault. Changes
in dip rate occur near the fault and sometimes at appreciable
distance away from the fault. The changes include drag and
rollover.
(4) Distorted dips seen through the fault may be an evidence of
faulting. A fault juxtaposes different parts of the earth.
Velocities differ along the fault line. The raypaths passing
through the fault plane are bent due to change of velocity to
different directions. This distorts the apparent dip for events
below the fault plane in an irregular manner.
( 5 ) Cut out of coherent events bsneath the fault plane takes place.
We normally recognise reflections by seeing same phase on a
xdjacent seismic traces, it adjacent ray paths encounter dif'crent
velocity contracts at the fault and are bent by different amounts,
the distortions become so rapid. This destroys coherency of
reflections.
(6) Shift of horizon along the fault pim. There is a shift of the
overall reflection pattern dong the fault plane.
These are used in interpreting faults on seismic sections. Along
the fault plane reflections with distiact character are offset on
opposite sides of the fault. In some situations distinctive
reflections cannot be correlated across the fault p ix : except
when the package of reflectioas is used. Fault plane reflections
occur and may not be reco,or,ised especialiy reflection from
steeply dipping fault planes. This is because the their evidence
is far from fault plane and the character may not be constant.
Faults cause misties of seismic lines. When we follow an event
around a loop of a seismic grid, misties may result due to faults. The
faults. The faults crossed may have different throws at different
locations or the throw may change laterally resulting in misties.
4.5 Sesimic stratigraphy.
According to Brown and fisher (1982), the integration of
seismic data with stratigraphic concepts is an advancement in basin
analysis. Seismic facie analysis is carried out using three dimensional
data and computer. The basic assumption is that seismic reflection is
inferred to represent an isochronous surface except where there is an
unconformity. Isochronous reflections may pass through many facies
identified by change in amplitude and frequency.
There are two approaches to seismic stratigaphy.
(1) A physical modeling of lithic and fluid composition utilizing
computer analysis of velocity, ampiitude, frequency and other
wave parameters.
(2) Stratigrapiiiclfacie approach using reflection szctions and
geophysical well logs. This is used in the interpetation of
lithohcies and subsequently depositional sequence.
Recognition of depositional systems on seismic proiiles permit
mapping of potentizl reservoirs, source and seal deposits. This
provides a basis far reconstructing the structural, depositional
and erssional history of the basin.
Prirnary reflections are in response to significant impedance
changes except for fluid contacts such as oil-water contact and
gas-water contact.
Unconformities are diachronous, though strata between them
constitute time-stratigraphic units. Stratal surfaces represent
conformable changes in depositional regime. The seismic response
to them is chronostratigraphic reflections. Reflections confonn with
collective configurations, continuities, velocity-density contrasts and
other physical properties.
Seismic stratigraphy is a direct detection technique. It is based
on the effect of porosity and fluid content on density and velocity.
The diagnostics used in interpretation of hydrocarbon reservoirs are
bright spots, phase reversals and variance of reflection dips fiom
structural dips in gas-oil, oil-water and gas-water contacts. This
technique is amplitude dependent hence amplitude conservation
processing is used during processing of the 3-D data.
4.6 Data wed in seismic Interpretatinn
It is pertinent to describe briefly some vital geophysical and
geological data used in seismic interpretation. There are other types
of data used for detailed geologic interpretation of seismic data. The
fallowing data are required, vertical seismic sections acquired from
the area of s w e y , well log data fiom a well within or close to the area
of survey, vertical seismic profile, synthetic seismogram, base map of
area of survey, and depth-velocity profile.
4.6.1 Seismic sections
Vertical seismic sections are obtained fiom the 2-D or 3-D
seismic data acquired fiom an area of survey. The acquired field data
is taken to the processing centre where the seismic sections used for
interpretation are obtained. Each seismic section gives the data for a
line of profiling. There are lines were shot along the strike while the
other lines shot along the dip to the horizon. This forms a grid of lines
covering the area where data was acquired. Migrated seismic sections
are used for interpretation as it presents a better image of the
subsurface.
4.6.2 Vertical seismic profile (V.S.P)
This is a seismic section made with shot on the surface while
the geophone positions were lowered down the hole usually a well.
A V3.P can be used to identi& an event on a seismic section. A
depth in the well can be located on the first break curve and reflection
at that point on the VSP can be matched with the one at the same
reflection time on the seismic section (coeffeen 1936). Where
available the VSP may be correlated with the seismic section to pick a
horizon at formation top.
4.6.3 Synthetic Seismo :ram
It is a seismic a, like trace produced fiom velocity infomation
in a sonic log. It partly bridges the gap between well data and seismic
data. Synthetic seismogram is made at the time scale of the section
but the depths can be plotted on the other side of the seismogram.
The formation tops from the well c m be plotted on the depth scale.
T.le reflection on the seismogram is expected to be strong at the
interface that produces it or gt a lag of about 30 to 60ms if tile
synthetic seismogram is of minimum phase. The reflection is similar
to the reflections of the seismic section hence on correlation, the
reflection character looks alike. When the reflections do not match
each other at the depth of correlation, the synthetic is slid up or down
within possible lag to find best point of ovcrall similarity of
reflections. The synthetic seismograms is used by an interpreter to
select the top of sand which will be mapped on the seismic section.
4.6.4 Base Man.
A base map of the survey area prepared by surveyors is
important to the interpreter. Base maps are prepared on transparent
material for easy reproduction. It contains information showing all
the seismic lines of profiling, the shotpoints, existing well locations,
political boundaries, company's lease and geographical location.
Contour map is produced using the base map. The reflection time will
be posted to the seismic line on the base map. Contouring makes
numerical data visual for recognition if low and high grdient areas.
The contour m:?ps hence gives a 3-D view of the survey area.
4.6.5 Wsll IOE 4 s
The geophysical well log d:cta is very important in seismic data
inteqrztation. It is used in producing cross sections. The well log is
useful in selecting the depth of top sand which when converted to time
can be located on the seismic section. In this way seismic - log
correlation is carried out to select strong reflections on the seismic
section which correspond to top of formaxion sand. In the absenca of
V.S.P. and synthetic seismogram the well to seismic ccrrelation is
used in selecting the strong reflection for picking on the seismic
section.
Geophysical well logging provides various types of data. These
include.
Self potential log data (SP). This is used for locating the boundary
between shale and porous bed (Telford et a1 1988). It utilizes
electrochemical effect which gives rise to voltage drop. Shale has
higher SP value than sandstone. The shape of the curve characterises
depositional sequence.
The grammar ray log is used in measuring the shale content.
This is because there is greater quantity of radioactive element in clay
and shale than in sandstone. It is used mainly where SP log is not
diagnostic especially in resistive formations. This is due to little
difference between salinities of mud and formation water or oil based
muds. Delta T or density log. It measures the transit time through the
porous formation hence it is used in determining the porosity of a
formation. The density log is useful in predicting over pressured
zones. The log value increases in the order of shale, sandstone and
pore filled with brine. The Neutron log is used in locating porous
zones and in determining the amount of liquid filled porous zone. It
utilizes the amount of hydrogen per unit volume or hydrogen index. It
measures porosity better than the density log.
Resistivity log measures resistivity at various depths. It is used
for marking out the boundaries between shale and sandstone. It is
useful when selecting the top of formation sand to avoid mapping
shale horizon on seismic section.
4.7 Seismic data interpretation sequence.
The general routine sequence of interpreting seismic data is
here outlined, however this is not exhaustive depending on the
interpreter and the detail of interpretation required.
4.7.1 Selection o f mapaing horizons.
The horizon to be mapped on the seismic section is important.
,This is because a horizon which represents the top of shale will not be
prospective for oil. Also a good horizon must have lateral continuity
across the survey area. The best horizon to be selected is that of the
top of an oil sand. The selection of mapping horizon involves mainly
three things.
Assembling geological data. Well logs are used to obtain the
boundary between shale and sands tone as could be obtained in a
resistivity well log. The porosity and fluid content of the selected
sand in order to map an oil sand horizon is determixed using other
well log data such as neutron log and spontaneous as potential log.
Therefore prospective reservoirs are identified and fluid contacts are
deterinined using geological data.
The geophysical data required include the fo\!owing the base
map of the sslwey area showing shot point location, velocity surveys
or velocity - depth profile of a well located within c- close to i:i< ile'd
and u~unarked seismic sections. It is pertinent to asce:xir! that all line
ties are defined at the top of each seismic scction. The pertinent
formation tops and total depth of the wells l o c ~ t d on or near the
seismic lines are spoted on the seismic sections.
Well to seismic correlation. Using the depth of the selected oil
smd formation and depth velocity profile a two way travel time is
obtained. The formation depth is determined on a wcll located on a
seismic line. The two way travel time obtained for depth of the oil
sand formation is then marked on the seismic section. This is used in
selecting the horizon to be mapped. However a synthetic seismogram
or V.S.P can be used to select the mapping horizon cin a seismic
section. In the absence of a good reflector at the level, a reliable
seismic event believed to be representative of the structure at reservoir
level can be selected. When the mapping horizon has been selected,
then interpretation of the seismic sections follows.
4.7.2 Interpretation of seismic sections.
The seismic interpretation of structures mainly involves fault
interpretation and horizon interpretation.
Fault interpretation is carried out fclrst on the seismic sections of
the dip lines. The dip lines are then tied with the strike lines to mark
the faults on the strike line. Faulting is noticed using seismic
diffractions and break in wavelets, also well controls help in
establishing the throw of faults, other factors due to faulting are
seismic data detoriation later followed by a strong event (reflection),
mistie of seismic reflection correlation and vertical displacement of
seismic reflection bands. The faults in all the dip and strike lines have
to be delineated before correlating reflection on the seismic lines.
Faults which are not identified could cause mistie especially where the
throw is large.
Following reflections on a horizon is another important part of
seismic interpretation. The continuity of reflection on a seismic
section is followed to the point where it ties with another line. The
interpretation is carried onto the line by tying at the point of
intersection. At such point the reflection on the two seismic sections
are similar and continuos. Interpretation across a fault is established
by using a package or band of reflections. The seismic section is
folded or juxtaposed to establish continuity of the reflection across the
fault.
In figure 4.1, the choice of which part of a reflection to pick is
shown. The peak is better and easier for an inexperienced
geophysicist. A 2B black pencil marker is adequate when the peak is
to be picked. When a coloured marker is used the trough is picked as
it shows the colour. Also the part of reflection to be followed depends
on if the processing is zero phase or minimum phase. In zero phase
processing, the use of the trough or peak is adequate while in
minimum phase processing, the use of zero crossing is better
especially where a coloured marker is required. Interpreted horizons
could be used as a check on each other as illustrated in figure 4.2.
When interpretation is completed on all the lines, the loop will tie
with the starting point. All the points of intersection in the grid of
lines will all tie. In figure 4.3, the sequence of loop ties starting fiom
a well is illustrated. When the loop doesn't tie, the error could be fiom
the interpreter or arise fiom a fault. The fault may not have been
identified or the proper throw on a horizon is not established leading
to the interpretation of a different horizon. It is also important to note
that when a loop ties, it doesn't mean that the interpretation is
perfectly in order. When the loop ties and the sections have been
checked, the two way travel time is measured ad posted for contouring
and mapping.
4.7.3 Fault mapping and contouring
The faults interpreted on the seismic sections ax-:: identified with
letters. These are posted to the base map. The throw of the fault is
established fiom the well control if available or a throw could be
established by "jump correlations seismic events across faults. Major
-- Cough -- -- zero crossing -- peak
fig 4.1. Choosing part of reflection to pick.
Fig 4.2. Using interpreted horizons as a c k c k on each other.
Fig 4 .3 . Sequence of loopties starting from a well.
.-..
I Fig 4.1, 4.2 and 4.3 picking and tying of reflect ions ( wilken 1990 ) .
faults are mapped using parallel dip lines. The fault traces of the
major faults are expected to conform with the regional structural
grain. Minor faults could follow the structural grain or trend in an
oblique direction. Where fault alignment options exist, preference
would be given to downthrown "concave" fault trace alignments as
opposed to "convex".
Where the two way travel time has been posted on the base
map, contouring is then carried out dter mapping the faults. The time
could be posted on the shot points r;r at the appropriate position along
the seismic line based on the contour interval (coeffeen 1982). In
most projects, a twenty millisecond contour interval is used in
mapping. Initial structural kame work could be established using
anticlines and synclines or by contouring at a 100 millisecond interval
initially. The subsequent filling in of the twenty millisecond intervals
and reshaping as required is then carried out. Map "smoothing" may
be desirable, and can be accomplished to a certain extent by arbitrarily
changing -two-way time values plus or minus two milliseconds. This
is within the accuracy limitation reading of two-way times fiom
seismic sections at a vertical scale of 2% inches per second.
In contouring, where options exists, highs are emphasized in
preference to lows. Attempts are made to continue structural trends
scross faults although some lateral displacement could occur. It is
important to check contouring adjacent faults, to determine that
throws are properly shown. Where dips are critical adjacent to f ~ l t s ,
values are placed on the map at location between shot points.
A comp1etedcontour map is rechecked for mechanical accuracy.
CHAPTER FIVE
INTERPRETATION OF 2-D SEISMIC REFLECTION DATA FROM
MEREN FIELD
5.1 Location of Meren field.
Meren field is located offshore in the Niger delta basin. The
field lies at the western edge of Niger delta. The depth of water
within the field is less than 200m. Tlie location map of the field is
shown in figure 5.1. The field lies between longitudes 4" 40'E and 6"
40'E and latitudes 5 20'N and 6 ' OO'N. Tlie total land area.. of the
field is about ten thousand square kiloinetres. Meren field lies close
to the mouth of Benin river into the Atlantic ocean. It is covered
under Oil mining lease (OML)95.
Tlie geology of Meren field was discussed in section 1.4. It is
however pertinent to know that the structural style of the western edge
of Niger delta offshore differs from the structural style in the southern
offshore depobelt. The delta edge is dominated by growth faults. The
presence of hanging wall and rollover anticlinal structures dominate
this part of the delta. This is unlike the southern offshore depobelt
where complex structures dominate the structural style. The faulted
anticlhes are found within Mere11 field with few complex structures.
The location of this field influenced method of data acquisition.
---1.-
-- - - . , -c-Y.- C. y , d--* -- . .C . , , ,.,: .,.:,.I -Shooting direction -+ bJ E%,Ci.. , . . . , . . . , ,
Fig 5.1 locatih map of Meren field.
5.2 Data acquisition
The 2-D seismic reflection data were acquired by carrying out a
marine survey.
A total of eighty two seismic lines were shot . These consist of
fifty four dip lines and thirty two strike lines. The dip lines were shot
in north east direction while the strike lines were shot in south east
direction. Thirteen seismic lines made up four strike lines and nine
dip lines were used for this project. The data was acquired by
compagnie general de geophysique (C.G.G) for chevron. In this
survey the energy source was vaporhoc, whose capacity is one octojet.
The depth of the energy source in water is 4.9.m. A shot point
interval of 25m or 2x50m was used for data acquisition
A floating or drag cable steamer at a depth of 4.2m in water was
used. A total of forty eight hydrophone groups were carried by the
streamer. The group interval is 25m while the number of
hydrophones per group is twenty four. The type of hydrophone used
is HC 202. The streamer has a total length of 1200m.
The data was recorded with SN338B instrument and the tape
format used is SEG B. A frequency of 125HZ,72dB/oct was used for
filtering. The recorded data was sampled at a rate of 2ms while the
recording length is six seconds. The recorded data on field tapes
were then taken to the processing centre.
5.3 Data Processing
The data used for this study were processed by (C.G.G), The
summery of the steps followed in processing is described here.
The SEGB recorded field data was demultipexed to sort out the
information into appropriate geophone channel outputs. The data was
94
subsequently resampled from rate of 2ms to 4ms in order to reduce the
volume of data that will be processed. The data was edited to
normalise and balance traces before gain recovery was applied to even
up and enhance weak reflections. Tlie data was sorted into CDP
gather and signature stabilization was carried out to minimum phase
using recorded vaporclioe signature. At the CDP stage of processing
line merging where necessary was done since a floating streamer was
used in shooting tlie lines.
Spiking deconvolution was carried out to compress the
effective source wavelet contained in tlie seismic trace to a spike. At
a window gap of 0.3 to 1.75 the operators length is l6OMS and pre-
whitening is 5%. At a window gap of 1.4-3.0s the operators length is
l6OOMs and pre-whitening of 5%. Tlie initial velocity analysis was
carried out using one velocity spectra at every Ikm. Using the
velocity analysis Nmo correction was then applied.
The traces were muted to eliminate shallow parts of the longer
traces and deeper parts of the short traces. The data was then stacked
using 2400% or 24 fold stack. Predictive deconvolution was carried
out after stacking at a gap of 24MS. A total operator length of 16OMS
and pre-whitening of 5% was used for both window gaps of 0.35 - 1.7s and 1.4s - 3.0,s.
The data was mib~ated so that events were taken to their true
locations. This is to enable the estimation of depths of the reflecting
interfaces to be made within tolerable error. Wave equation migration
was used on this data.
To restrict the time to the given set of frequencies the data was
again filtered using time variant filter. At a time interval of 0.0 to
0.65s, the frequency window is 10,15-70,90 Hz. At a time interval of
1.2-1.8s, the frequency window is 10,150 60, 80Hz. While at a time
interval of 3.0-5.0s fiequency window is 8, 12-40, 50Hz. The
dynamic equalization was then carried out with a single data and
design window of 0.3-3.0s.
The data was displayed with a polarity in which a compression
wave at hydrophone was recorded as negative number. The negative
number was displayed as trough (white), while the positive number
was displayed as peak (black). Horizontal scale of the seismic section
is 1:12,500 while the vertical scale is Sincheslsecond. The seismic
sections were used for geologic interpretation.
The data used for the present study was a subset of the data
acquired by chevron Nig. Ltd. in the Meren field. To be specific, the
sections used in this project consists of four strike lines and nine dip
lines.
5.4 Interpretation Of Data
5.4.1 Examination Of The Data
The geological data used for the interpretation was the well log
of M-73 well. This well is underviated. The well logs were those of
resistivity, gamma ray and interval transit time. The well log shows
that the depth interval of logging from 2100ft to about 4000ft gives
very low resistivity, high delta-T value and low gamma ray value.
This represents the saline fluid in the continental alluvial sand of the
Benin formation. The interval of 5150ft to about 8900ft gives at
certain depths high resistivity value, low interval ,transit time and high
gamma ray value. In this depth interval the shale and sandstone
Fiq 5.2 sectbns of well log of M-73 well (chevron 1982).
boundaries could be demarcated. In this interval the paralic clastics of
Agbada formation was observed. The Agbada formation sand is
pierced by shale, clay and silts in various proportions. The depth
interval from 9000ft to about 9700ft give low resistivity high gamma
ray value and low interval transit time. This shows the top of Akata
formation composed of shales and silts with few streaks of sand. At
such sand depths high resistivity obtained with low gamma ray value.
The sections of M-73 well log are shown in fig. 5.2.
The geophysical data used in the interpretation were vertical
seismic sections, velocity - depth profile of M-73 well (table 5.1) and
the base map of the survey area. The position of the well, M-73 was
located on the seismic line - 14. The positions of intersection of
seismic lines were marked. All the seismic sections were migrated
except the line - 14 which is a strike line. The seismic lines were
marked on the base map. The shot points were located and their
interval on the base map was examined to correspond with interval on
the seismic sections. In a situation where the interval of incorrect
intersection is small, it was neglected. However intersection error
could result from original navigational data.
Based on the quality of 2-D reflection data the quality of
reflections on the seismic sections interpreted was fairly good
generally. However in the interval 0 to 1 looms the reflections were
discontinuous. Most of the faults terminated at the base of this level.
This interval on the seismic section represents the Benin formation as
shown in the well logs.
The data in the interval 1300ms to 240ms is of good quality.
The reflections were found to be continuos and of relatively high
amplitude. Most of the faults lie within this interval. It represents the
LEVEL MEASURE NUMBER DEFIX
FROM KB FI' t
1 143 .O 2 2150.0 3 2790 . 0 4 3242 .0 5 3400 .0 6 3 5 0 0 . 0 7 3924. 0 8 4382. 0 9 4724. 0 10 5154. 0 11 + 5410.0 12 5866.0 13 61 12.0 14 6435.0 15 6608.0 16 7 0 0 0 . 0 17 7415.0 18 7912.0 19 8305.0 20 + 8630.0 21 8750.0 22 9040.0 23 9410.0 24 9800 .0 25 10100.0 26 10640.0 27 11240.0
VERTIC VERTIC OBSERV VERTIC VERTIC AVERAGE DELTA DELTA DEPTH TRAVEL TRAVEL TRAVEL TRAVEL DEPTH TIME TIME FROM FROM TlME TIME TJME SRDIGEO BETWEEN BETWEEN
SRD GL HYDIGEO SRUGEO SRDIGEO SHOTS SHOTS FT FT MS MS MS FT/S FI' MS t t
62.0 0 12.40 12.40 12.40 5000 2069.0 2007.0 341.25 342.71 342.71 6037 2007.0 330.3 1 2709.0 2647 .O 429.48 431.46 431.46 6279 640.0 88.75 3161.0 3099.0 486.33 488.55 488.55 6470 452.0 57.09 3319.0 3257.0 506.41 508.69 508.69 6525 158.0 20.15 34 19.0 3357.0 521.92 524.23 524.23 6522 1 0 0 . 0 15.54 3843.0 3781.0 576.67 579.12 579.12 6636 424.0 54.89
4301.0 4239.0 63 1.62 634.19 634.19 6782 458.0 55.07 4643.0 4581.0 678.53 681.16 681.16 6816 342.0 46.98 5073.0 5011.0 726.74 729.45 729.45 6955 430.0 48.29
+ 5329.0 5267.0 756.48 + 759.23 + 759.23 7019 256.0 29.78 5785.0 5723.0 807.95 810.76 810.76 7135 456.0 51.53 6031.0 5969.0 835.39 838.23 838.23 7195 246.0 27.47 6354.0 6292.0 870.49 873.37 873.37 7275 323.0 35.13 6527.0 6465.0 888.43 891.32 891.32 7323 173.0 17.96 69 19.0 6857.0 927.92 928.85 930.35 7433 392.0 39.53 7334.0 7272.0 %4.62 965.58 967.58 7580 415.0 36.74 783 1.0 7769.0 1015.04 1016.04 1018.04 7692 497.0 50.45 8224.0 8 162.0 1058.73 1059.75 1061.75 7746 393.0 43.71
+ 8549.0 + 8487.0 1090.31 1091.35 +1093.35 7819 325.0 3 1 .GO 8669.0 8607.0 1100.43 1101.47 1103.47 7856 120.0 10.13 8959.0 8897.0 1126.69 1127.75 1129.75 7930 290.0 26.27 9329.0 9267.0 1161.26 1162.34 1164.34 8012 370.0 34.59 9719.0 9657.0 1197.57 1198.66 1200.66 8095 390.0 36.33 10019.0 9957.0 1223.89 1224.99 1226.99 8165 3 0 0 . 0 26.33 10559.0 10497.0 1281.61 1282.73 1284.73 8219 540.0 57.74 1 1 159.0 11097.0 1346.78 1347.92 1349.92 8266 6 0 0 . 0 65.19
INTER' VELOC BETWEEN
SHOTS FT/S
TABLE 5.1 DEPTH - VELOCITY PROFILE OF M- 73 WELL (CHEVRON 1982).
Agbada formation as obtained in the well logs. The quality of
reflections in the interval 2500ms to 4000ms was found to be poor.
The reflections were distorted and discontinuous. The data was
dominated by low frequency reflection packages. The interval
represents t$e Akata formation hence the processing of data at such
level may not be of much importance. The faults terminated at the top
of this interval.
Two strong seismic events were observed at the time interval of
100 to 150ms. These events had a strong amplitude and represent the
direct waves arriving at the receiver from shallow depth. A section of
line 14 is shown in fig. 5.3. The quality of reflection at various time
intervals were shown. The depth - velocity profile of M-73 well is
shown in table 5.1. The profile was combined with the well log to
select horizons mapped on the seismic section.
5.4.2 Well Log -To-Seismic Correlation
he well-to-seismic correlation method was used in selecting
the horizons mapped on the seismic sections. The resistivity log was
mainly used to obtain the boundary between shale and oil sand. The
gamma ray log and the interval transit time log were used to pick a
good sand-stone formation. A combination of the three log values was
used in deciding the depth of top sand selected for mapping.
The depth of top sand for horizon I was selected at 5410ft
(1623m). When the kelly bushing (KB) height of 81ft (24.3m) was
removed, the sea reference depth (SRD) of j329ft (1598.7m) was
obtained. The selection of this top sand was based on the following
values. The resistivity log of 20 ohm-m, gamma ray value of 36
GAP1 and interval transit time (AT) log value of 75psIft. These are
shown in sections of M-73 well log in fig 5.3. The depth-velocity
profile shown in table 5.1 was used to obtain the one way travel time.
At a vertical depth from SRD of 5329A, the one way travel time
(vertical) is 759.23 ms. This value was doubled to give 15 l8.46ms
which is the two way travel time on the seismic section. The top sand
depth of the second horizon was taken at 8630ft (2589.0m).. When
the kelly bushing (KB) height was removed, the vertical height from
SRD gave 8549ft 2565.7m). The two way travel time obtained for
this depth is 2186.70 ms. The log values at the top of this is and level
are as follows; A resistivity value of 9 ohm-m, gamma ray value of
60GAPI and interval transit time (AT) of 80psIft. Using the two way
travel time the second horizon was selected on the seismic section.
At the position of M-73 well on seismic section of line-14 a
vertical line was drawn to the level of the two horizons. The positions
corresponding to the time for horizon I and the time for horizon I1
respectively were annotated along the well position. This was
illustrated in fig 5.3. The use of this method may not locate
accurately the formation top on the seismic section hence the strongest
reflection close to the position annotated for each of the horizons was
mapped. The method was used because vertical seismic profile or
synthetic seismogram were not available. When the horizons to be
mapped were selected, fault and horizon interpretation on the seismic
sections were then carried out.
5.4.3 Interpretation of faults
The dip lines were used for interpretation of the faults. The
evidence of faults on seismic sections has been discussed in section
4.4.4. These were used as a guide in picking the faults on each
Fig 5.4 faults and horizons interpreted on seismic section.
seismic section. The faults interpreted were labelled as B, C, D, Dl,
D2, E and X as showdin fig. 5.4 . The faults X, Dl and D2 are the
minor faults while B,C and D are the major faults. The major faults
cut through the two horizons mapped. The faults interpreted are
normal growth faults. The faults interpreted on the dip lines were
used in locating the faults on the strike lines. To do this, strike lines
were tied to the dip lines at the point of intersection and the fault
positions were marked.
To identify each fault and label them on subsequent parallel dip
lines, two closest parallel dip lines were used. One of the seismic
sections is folded horizontally and laid on top of the other such that
the faults on both seismic sections are found to match each other at
their respective positions. The faults were then identified and
labelled. The termination of reflection packages on each fault may
look similar on parallel dip lines where such fault cuts across. In
many situations the position of the faults shift from one seismic
section to the other. The blocks of sediment deposition and
subsequent faulting was shown by the termination of reflections. The
&ow of the faults and continuity of reflection across the fault is
obtained by folding the seismic section across the fault and correlating
packages of reflection and nature of wavelets.
When all the faults on the seismic sections have been
interpreted and tied properly, the horizon interpretation was then
carried out.
5.4.4 Picking reflection on horizons
The events on each of the two horizons selected were found to
have good lateral continuity across the seismic sections. The
reflections on each of the two horizons were picked after
interpretation of faults. Picking of reflection started from the well
position on line -14. The part of reflection followed is the peak using
a 2B pencil. The horizon interpretation moved from well position to
the intersection of L-14 with seismic line 42 which is a dip line. The
interpretation was carried to the dip line by tying the two sections at
the point of intersection. The reflection was then followed to the next
point of intersection. In this way interpretation of the horizon was
carried round the entire grid of lines forming the loop.
At fault positions, the reflections terminated and wavelets were
found to split. The continuity of reflection along the horizon was
determined by folding the seismic section across the fault and
correlating packages of reflection above and below the horizon. The
dsplacement and character of reflection package were used in
determining the throws of the faults. Also where reflections were
weak and not clearly visible; the seismic section was folded and the
reflection package was used to determine continuity of reflection.
The two horizons interpreted were carried along together. This
acted as a guide in following reflections. The relative separation was
found to be nearly equal along the seismic lines. The change in
separation where it occurred was gradual and consistent.
When interpretation was completed on all the lines, the loop
was checked at various points of intersection for proper tying of lines.
The positions of mistie were interpreted again until all the lines were
found to have tied. It would be noted that misties which occurred
could have resulted from inaccuracies in the original data, difference
in wavelet at intersection, unequal throw of faults, adjustment made
during processing and wrong interpretation.
5.4.5 Horizon and fault mappinz
A time contour and fault map was produced for each of the two -+
horizons interpreted . The faults and time contours were mapped
together on the same base map.
In these maps shown in figures 5.5 and 5.6 the two way travel
times were posted to the shot point locations. The disadvantage of
using this in contouring is that the spacing of contours can not be
accurate. This is because contour values which lie between two shot
points will be fixed by approximation while drawing the contours.
The other method is to post time values at their exact positions along
the seismic lines on the base map. The time values posted here are
those whose values fall within the contour interval being used. The
contcur interval used in this work is 20 ms. The time was therefore
posted on all the shot point locations and at the positions of the &act
contour value along the seismic line on the base map. The faults were
also posted on each seismic line on tlie base map. The down throw
and up throw of the faults were indicated. The space between the
down throw and up-throw of each fault depends on the throw of that
particdar fault. Each fault posted was identified with it's labelled
letter. The major faults had a bigger throw than the minor faults.
The faults were fxst mapped. In this the up-thrown sides of a
particular fault were joined from one seismic line to th:: other. Also
the downthrown sides were joined in a similar way. The fault
curvature of each fault was smoothened on the base map. The faults
were found to have a concave curvature towards the downthrown side.
In the map of horizon I fig. 5.5, the faults x and Dl terminated on the
major fault D. The minor faults were only found in horizon I. They
died out before the deeper horizon 11. The throws of the faults were
highlighted in mapping. The major faults had a bigger throw than the
minor faults.
Faults are important not only as structural traps but also in tying
contours. Therefore the faults were properly mapped before
contouring.
The contour interval used in the map is 20ms. The structural
pattern was worked out using anticlines and synclines before
contouring. The contour was drawn by joining equal values fiom one
seismic line to another based on the contour interval. A contour
rounded where it joined itself. Some of the contours terminated on a
fault while those at the extreme were drawn to terminate outwards.
The highest contours were drawn first and contouring conticued
outwards to lower areas. The high gradient areas were worked out to
locate closures correctly. Also closures against faults were carefully
drawn especially the faulted closures. The highs were made rounded
while lows were made angular.
To contour across a fault, the throw of the fault was considered
as the contours were not continuous on the same position across the
faults successive contours were made to run approximately parallel to
each other from one position to the other in an area, the relative
spacing of the contours depends on the position of the contour value
along the seismic line.
A time contour map was produced for each horizon interpreted.
The map gives a 3-D view of the subsurface mapped hence closures
can be located. This was used by enables the interpreter to make
recommendations and draw conclusion.
5.5 Comments, recommendations and conclusions.
5.5.1 Comments
The seismic sections interpreted revealed the tripartite
stratigraphic sequence of the Niger delta. The interval 0-1 100ms on
the seismic section was dominated by high frequency and
discontinuous reflections. The section represents the Benin formation
composed mainly of continental alluvial sand containing saline water
as shown in well log (fig 5.2). The interval from about 1300ms to
2400ms consists of continuous strong reflection events of high
amplitude. The faults in this interval were identified. The section
represent the Agbada formation based on well log interpretation in
secticn 5.4.1.. This is the hydrocarbon bearing sequence of the Niger
delta. The two horizons interpreted were selected from this interval.
The deepest part of the seismic section from 2500ms to 4000ms
consists of poor data. The reflections were discontinuous and consists
of low frequency package. The interval represents the top of Akata
formation. This consists mainly of shale and few streaks of sand. The
faults terminated mainly at the base of Benin formation. They passed
through the interval of Agbada formation to terminate at the top of
Akata formation.
The interpretation shows four major faults (B,C,D and E) and three
minor faults (X,Dl, and D2 ). These are shown in figure 5.3. The
faults are normal growth faults.
The two horizons interpreted also revealed existence of simple
rollover anticlinal structures. The rollover structures terminated
against the downthrown side of the normal growth faults. There were
faulted anticlinal structures on both horizons interpreted.
The contour map of horizon I shown in figure 5.5 revealed that
the horizon dips in a direction from northeast to southwest. The time
value for the shallow part northeast is 1380111s while the time value for
the deepest part on the horizon is 1740ms at the southwest. The
major faults identified on horizon I are C,D and E which are the major
faults. The minor faults on the horizon are X, Dl and D2 . These
faults gave rise to the faulted closures identified on horizon I.
All the faults on horizon I are found to be concave towards the
downthrown side. This agrees with the regional structural geology of
Northwestern part of Niger delta offshore. The faults were; oriented in
a direction northwest to southeast.
The closures identified on the contour map of horizon I (fig. 5.5
were numbered. Seven closures were located on this horizon.
Closures (1) and (4) are located at the southeastern part of the survey
area. The closure (1) is below the downthrown side of fault D. The
contours round it move outwards to low gradient area. The closure
cut across three seismic lines which on examination does not show
high amplitude anomaly. The value of the closing contour is 1460111s.
Most closures at the downthrown side of normal faults contain high
gas to oil sand ratio. Closure (1) may not contain a high volume of oil
sand. Closure (4) is against the upthrown of fault C. It lies between
the faults C and E. The value of the closing contour is 1400 ms. The
amplitude anomaly on the seismic section shows the closure as a
good hydrocarbon trap. Closure (2) is located at the southwestern part
of the surrey area. The contour values of this closure is 1480ms. The
amplitude anomaly on seismic section shows that it is a good
hydrocarbon trap. Closures (3) is located at the central part of the
survey area. The contour value is 1480ms. It is located between
faults Dl and D. The seismic sections shows that the closure is a good
hydrocarbon trap. Closure (5) is a faulted closure. It lies at the
northeastern part of survey area. Three faults X, C and E cut across
the closure. The seismic sections shows high amplitude anomaly
hence the trapping of hydrocarbon will be by combination of the fault
and the anticlinal closure. Closures (6) and (7) lie on the northwestern
part of the survey area. These closures are unfaulted. Closure (6) has
a contour value of 1460ms, while closure (7) has a contour value of
1540ms. The amplitude anomaly on seismic section shows that the
closure (6) is a good trap. Closure (7) lies between the faults D and C.
The closure cc vers a large lateral area. The closure is a good
hydrocarbon trap, however the low areas further northwest shows that
dry well could be encountered in that side of the closure.
The interpretation of horizon I1 shows that only the major faults
By E, C and D cut across this horizon. The horizon is deeper hence
the minor faults died out before reaching the horizon. The faults gave
rise to faulted closures observed on the horizon.
The contour map of horizon I1 (fig 5.6) revealed that the
subsurface layer dips in a direction from northeast towards southwest.
The shallow part of the northeast had a minimum time value of
1920ms while the deepest part southwest had a time of 24OOms.
The faults on the horizon were found to be concave towards the
downthrown side. The orientation of the faults is from nonvest to
southeast.
Five closures were identified on this horizon. Closures (1) is
located at the southwestern part of the survey area. The contour
value is 2140ms. The contour closed against the downthrown side of
fault D. The closure against the downthrown side of a fault does not
prove to be a good oil trap hence gas well may be obtained if drilled.
Closures (2) and (4) are located in the eastern part of the survey area.
Closure (2) is faulted by the faults C and E. The seismic sections
shows there is high amplitude anomaly. The contour values ranges
from 2000ms at the downthrown of fault C then 1980 mg at the
downthrown side of fault E to 1960ms at the upthrown side of fault C.
The hydrocarbon trapping will be by combined effect of the fault and
the anticlinal structure. Closure (4) is against the upthrown side of
fault B. This upthrown closure is a good hydrocarbon trap. It shows a
strong reflection on the seismic section. Closure (3) lies between two
faults (C and D), it covers a large lateral area. The closure has
rounded contours around it. The contour value is 2020ms and it
shows strong reflection on the seismic section. The closure proves to
be a good hydrocarbon trap. Closure (5) is located at the northern part
of the survey area. It lies between two faults (E and B). The contours
around this closure are rounded. Also there was a high amplitwk
contrast on the seismic sections examined for this closure. The
closure was taken as a good hydrocarbon trap.
5.5.2 Recommendations.
The recommendations made here are ba eductions made
from the available data and the need for further studies.
The closures identified on the contour map of horizon I shows
that positions (3), (4), (5) and (6) are highly prospective for
hydrocarbon and are recommended for drilling. The closures (I), (2)
and (7) in horizon I would require further studies to determine where
wells could be positioned to avoid drilling dry gas wells.
Closures (2), (4) and (5) in the contour map of horizon I1 are
considered highly prospective hydrocarbon traps hence recommended
for drilling. Closures (1) and (3) will require a detailed study using
cross sections to properly position wells in order to drill wet wells.
It is also recommended, that a 3-D survey or an improved
seismic reflection survey should be carried out in the area. This is to
obtain a data of higher quality. The data obtained will be used in
carrying out lithostratigraphic sequence analysis and to determine the
hydrocarbon content in the identified closures.
Cross sections and geologists isopach map need to be produced in
order to properly position wells and determine the oil sand volume.
5.5.3 Conclusion
The structural interpretation carried out using 2-D seismic
reflection data from Meren field has revealed that the structural style
of the area consists mainly of normal growth faults. The orientation
of the faults is from northwest to southeast. The structural traps found
were mainly simple rollover anticlinal' closures, faulted anticlines and
closures against faults.
The well log data and reflections on seismic sections shows that
most of the closures are good hydrocarbon traps. Drilling of wells
was therefore recommended at the locations of these closures. The
hydrocarbon structural traps found shows that Meren field is a good
prospective area for oil and gas.
REFERENCES
Anstey, NA; 1977 Seismic interpretation- The p l~~s ica l aspects. I.H.R.D. (1.4) Boston USA.
Avbovbo, A.A, and Ogbe F.A; 1978 Geology and hydrocarbod productive trends of southern Nigeria basin. Oil and Gas Journal V. 76 no.48 P.90-93.
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